Monty, there's nothing wrong with doing an organised tour, especially if you're not confident for your first trip or if you don't want the (sometimes) hassle of organising your accommodation and transport. Plus, you have the chance to see where you'd like to go back to and spend more time, so that's a bonus!
A few things for you to consider while you're on tour:
Lauterbrunnen - my favourite place in this part of Switzerland (my other one is Luzern, which you might have some time in, but if not - the Paris to Lauterbrunnen drive is an all-day affair - then add it to your "next time" list) is a gorgeous town in a valley at the base of the Jungfrau. As you'll be there in Winter, I'd imagine you're thinking of skiing/boarding, which is ideal. Your tour may already have this included or as an option, but if not look up the ski info on the web for places like Wengen or Murren as there are no lifts directly from the mountains into Lauterbrunnen. Grindelwald is just around the mountain and there is also the Schilthorn just up from Murren, so you have plenty of options. Things to eat/drink - Rösti (all types from each region are great), Raclette (melted cheese on potatoes, can be hard to find but worth it), Fondue (cheese of course!), Eichhof beer (brewed just down the road in Luzern).
Florence - not too much hidden hear in the way of sights, so make a list of what you want to see and work your way through it (Uffizi, Bargello, Accademia, Duomo, Santa Croce). The joy of Winter is that there are less people, but in Nov/Dec there are actually still a lot of people (locals and tourists) around so if you can book ahead for the Uffizi you'll save time standing in line. Your tour might have this included (although usually not) so I'd check with your guide/director on the first day of tour as to times in the city and then get on line or call them to book it if you're interested in going. As for food...where to start?!!! Try Ribollita (Tuscan winter soup) and possibly the largest T-bone steak (Bistecca Fiorentina) you'll ever encounter at Da Fagioli (traditional trattoria on Corso dei Tintori, towards the river from Santa Croce), there's also great Ailimentari (delicatessens) around the city to buy cheese, salami (try the Florentine one dotted with fennel or Cinghale - wile boar) and other snacks. Have a walk down Via di Neri as there are some great wine bars, lunch spots and gelateria (some close for Winter however) to discover - this is a "locals" street, even though it's not far off the main thoroughfare.
Rome - again, where to start?! With potato pizza! There are quite a few Forno (bakeries) dotted around town, but three of the best are near sights you'll probably want to see. Two are near the Trevi fountain, on the way to the Pantheon along via della Muratte (I think. It's the street that runs off to the left if you're standing facing the front of the fountain) and also along via Pastini, just before you reach the Pantheon coming from the Trevi. The other one is over near the Vatican, never known the name of it but it's the third street on the right when you walk from St Peter's to the Vatican Museum entrance, there's a newsstand on the corner. Potato pizza is amazing, but there are all sorts of other toppings to try, and these places will cut the pizza to the size you want, so you can have lots of different ones - fabulous!
Venice - such a labarynth of a city that giving directions here is difficult, but what I'd suggest is keeping off the main squares (esp St Mark's) if you want to save money (otherwise treat yourself with a Euro8 cappuccino sitting outside Caffe Quaddri if it's sunny) and wander a little towards the Rialto (and off to the right) for some great trattoria, just avoid any with "tourist menu" as whilst the food will be fine, it might not offer the experience you're looking for. I'm a big fan of the Belini - peach juice and champagne/prosecco, but in winter these can be hard to find. As far as other drinks go, beers include Nastro Azzuro, Moretti and Peroni (who make Nastro Azzuro). Wines are plentiful, so try Chianti and Vernaccia in Florence (if you want to splurge, try a Brunello di Montalcino), Pinot Grigio, Soave and Cabernet Merlot in Venice and Rome is known for Frascati, but I find it a little flavourless, so try Orvieto Classico (white).
Salzburg - as you're only here one night, enjoy wandering the streets whilst snacking on a Mozart Ball (heard the music, got the t-shirt, now eat the chocolate!). If you have a free night, seek out a schnitzel (you are in Austria afterall!) and try soup with savoury pancake strips or dumplings (filling and warming) somewhere groovy (if it has "stuberl" in the title it will be a good local restaurant/pub).
Prague - Such a great city and some much to choose from. I love the Jewish Quarter for the history, and you can wander quite happily from the Old Town across Charles Bridge and up to Hradcany (the "ant trail" but it must be done). But don't over look Kampa Island (to the left of the bridge as you get to the castle side) for cute pubs and bistros, and you can visit the first pub Pilsner Urquell was served in Prague called
U Pinkasu which is just behind Wenceslas Square (the Old Town end, not the museum end). It has great Czech food and gets quite busy with locals and visitors around 7pm. Otherwise, trek down side streets in the Mala Strana (Little Quarter) on the castle side of town for some hidden gems. And if you see
smazeny syr (fried cheese snacks) on the menu or at a street stall, eat them! Great with beer! Pilsner Urquell is everywhere in Prague, so other beers to try are Budvar, Velkopopovicke, Staropramen, Kozel, Gambrinus - some of which can be hard to track down. Generally, pubs will have only one local beer on tap (they are "sponsored" by the brewery) but some have a choice, otherwise I guess that just means you have to move from one to the next to sample some! You'll also find Absinthe bars tucked away along with a drink called Becherovka which is a bitter-sweet, yellow herbal liqueur that Czechs drink for health, but it's strong so watch it. And watch the Absinthe. Whilst it doesn't have the wormwood in it anymore, too much will still make you see stars. And make sure you drink it properly - with the sugar and water, otherwise it will taste bitter and ugly.
Berlin - Currywurst! Curry-flavoured sausage that sounds odd but is a Berlin tradition. It is served everywhere, but some good ones are in the eastern side, particularly Konnopkes Imbiss – small Imbiss/Snack stand on cnr Danzigerstr & Schönhauser Alle, Prenzlauer Berg, by the Eberswalderstrasse station under the U2 line as it has been in the same family since 1930. Another Berlin institute is Schlemmermeyer on Tauentzienstrasse 16, just down from Ka De We department store. It's good for Wurst and other German fare and is cheap and delicious. The Hackescher Markt area is great for bars, clubs and general going out as is the Mitte area, so just wander past and listen for the tunes you like.
Berlin Beers: Berliner Pilsner and Berliner Burgerbrau are the two best, otherwise Berliner Kindl and Schultheiss are from Berlin but not as popular. Two sights I love are the Fernsehturm (TV Tower) on Alexanderplatz (Alex to the locals) and the Neue Wache (New Guardhouse) just near the Humboldt University. The Denkmal für die Ermorderten Jüden Europas (Memorial To The Murdered Jews Of Europe – Holocaust Memorial) is an amazing sight too and definitely worth a visit.
Amsterdam - again, so much to do by day and night. Food wise, try Kroketten (mashed potato logs with shredded beef coated in breadcrumbs and fried), Frites mit Mayonnaise (Fries with mayonnaise - amazingly good!), Poffertjes (Dutch mini pancakes) and Kip Satay (Chicken Satay - one of the now national dishes of the Netherlands!). Dutch beers to try are Heineken (of course), Amstel (much better than Heineken IMHO), Orantjeboom, Grolsch and Palm (from the south, not always able to find in Amsterdam). I love the cafe next to Oude Kerke on Dam (the palace square) for it's Kroketten, but you can also get them from a place called Febo (pronounced Faybo) which is like a slot machine fast food place and has branches dotted all over the city (open late a night too, obviously). There's also a cool cafe called Palladium on Leidseplein that serves a mix of Dutch and modern food. There are lots of good bars and a few clubs on Rembrandtplein and a lot of people end up at Escape club for a dance night out.
Paris - again, one of those places it's hard to recommend things for unless we know what you're specifically looking for...but I'll try. Definitely visit the museums (Louvre, Musee d'Orsay - my favourite along with the newly re-opened Orangerie with Monet's Waterlilies series and a raft of Impressionist and Post-Impressionist works downstairs) and hunt out the lesser-known ones like Rodin's Museum and Gardens (even a morning coffee in the gardens surrounded by statues if you're not into art is stunning), Notre Dame bell tower (great views) and even the Musee du Vin (wine museum...with tastings!). There are also great and funky places to eat, drink and be merry. Try the restaurants/bistros up at Montmartre (to the left of Sacre Coeur), Buddha Bar for swish cocktails (get there before 8pm to score a seat at the bar and dress well), great bars and bistros in the Latin Quarter (between Odeon and St Michel are some great side streets to explore). I could go on, but that should start you off. There's also some great info by
francefiend here:
docs.google.com/View?docid=dgjgmmgp_156cwprwh to help you plan your visits to Paris.
I hope that gives you a start for things to explore, either on your tour or when you go back by yourself. You seem to understand that your time on the tour will be limited so you're off to a good start. Enjoy the tour and let us know how it went, plus all about your independent travels once you're settled in London.