Welcome to GFE,
hemple.
As you've already been to Europe, I'm guessing that's the reason for the omission of some places (Prague, Florence) or less time in other places (eg Rome), but I can suggest the following:
Luxembourg - you may find that 1 full day (2 nights) or even 1 night if you arrive early from Brugges/Bruges and have the rest of that day and some time the next day before departing for Bacharach. 2 full days might be a little long in that particular city.
Germany - starting at Bacharach, which is a good choice, will give you a chance to see a little of the Rhein, and you can even look into a river cruise for a few hours (head north to Cologne and explore there for the full day before catching the train back) if you want to experience the scenery (check
www.kdrhine.com or
www.k-d.de ). Or you could even get on the cruise at Bacharach on the day you're going to Heidelberg, sail up (but south) the Rhein to Rüdesheim am Rhein (not far) or further along to Mainz then catch the train to Heidelberg, sightsee and have the night there before a little time the next morning and continuing by train to Rothenburg ob der Tauber (
NOTE: make sure you use this as a destination when searching on German train sites as there are two other Rothenburgs (one on the German/Polish border, the other up near Leipzig) and you want the one on the River Tauber, which is often shown as Rothenburg o.b.T.
NOTE: the KD Cruise boats accept Eurail passes as a travel ticket, which might help for the full boat trip Bacharach to Mainz then the train to Heidelberg as it is activated as a day of use and the boats are considered a form of transport akin to the train.
The train from R.o.b.T to Munich will be between 2hr45 to 3hr15 and involve a few changes, so you can get an early start and make the most of arrival day in Munich, thus sneaking in a little extra time. Or take the extra day from Luxembourg and add it to Munich, giving you 4 nights/3 full days allowing for your trip to Berchtesgaden (which could also be done from/on the way to Salzburg), half day at Dachau, day trip to the Ludwig II castles (Neuschwanstein, Linderhof, Hohenschwangau) and time in Munich itself (a great town).
And something worth knowing - if you odn't want to use the days on your Eurail pass for the day trips from Munich, there is something called a BayernTicket (or on weekends the Schönes Wochenende ticket) which is for train and bus travel in the state of Bavaria on most routes. The group ticket (more than one person) is Euro 25 (or may now be 29) from ticket machines in the stations, or Euro27 from the travel centre ticket office in the station. This may help with keeping days on your pass for travel days in the future.
www.bahn.de/regional/view/bayern/bahnregional/freizeit/bayernticket.shtml Cesky Krumlov - the train from Munich to CK takes around 7hr30mins, so either look at a night train on this section or add another day to CK if you feel you really want to sightsee. Otherwise, 1 full day will be good.
Vienna - you may want an extra full day here as there is a lot to see and experience and just one day won't really give you much time. The train from CK to Vienna will take 4hr30 with a few changes, so if you get an early start on the travel day, you'll have a good portion of the afternoon of arrival in Vienna, but still may find you need the additional full day, ie 2 full days.
Vaduz - you'll find you only need 1 night here as it's small and easy to walk to see the sights (you can even see the castle from the main street, so don't have to walk up to the gates).
NOTE: there is no train station in Vaduz, just bus services. So from Austria you'll train it to Feldkirchen on the Austrian/Lichtenstein border, take the bus into the Zentrum (centre) of Vaduz, then a bus out to Schaan-Vaduz station to catch the train to Switzerland.
Luzern - it's a stunning town so I'd choose here rather than Appenzell if it were me. And if you have 2 nights - 1 full day you could also take time to wander the city, cruise the lake (stunning scenery).
Bern - I like Bern, but feel that 1 night here would be enough for you, so take the day from here and add to Luzern.
Interlaken - not sure what your interests are and what you plan to do, but you might find that heading a little further into the mountains around Lauterbrunnen might work better for you in terms of scenery, activities, etc. Interlaken has a lot of adventure activities, but in terms of staying "in the mountains" you can't beat Lauterbrunnen, Murren and around the area. There are hostels in L'brunnen and Murren and a campsite (with cabins or a dorm) in L'brunne, so you'll find accommodation if you book well ahead (ie now!).
NOTE: I'd consider travelling from Vaduz to Bern, then Berner Oberland/Interlaken, then Luzern and travelling to CT from Luzern as the trains are a little more conducive to travel (there is an 8am-ish train with only one change in Milan then on to La Spezia for the regional train to the 5T). Otherwise, remember that if you catch a later train, the regional trains along the 5 villages stop around 11.10pm or sometimes the last one is 00.50 and the next isnt' until around 5am the next day, so don't arrive at La Spezia Centrale too late in the day.
Rome - the train will take a good chunk of your day from CT to Rome, unless you take the Eurostar Italia between Florence and Rome (1hr30mins), but 3 full days in just Rome will allow for a good amount of exploring, sightseeing and eating.
Other than that, you've put together a good itinerary. See what you can do with the above suggestions and no doubt the others will chime in with some more ideas soon.