Hey
WT,
first thing that popped into my head was Prater - and Herrbert has it covered too! Prater (or
Volks Prater) is a great place and his suggestion to visit in the evening is a good one. There are amusement rides, food stalls and a few beer halls/restaurants scattered over the park. The food isn't too expensive out here either, although you'll pay a little more if you sit inside rather than grab something and wander around. It's like a mini-Oktoberfest without the drunken tourists!
To add to Herrbert's excellent suggestions, here are my lucky 7:
1. visit the
Hofburg as well as
Schoenbrunn Palace - both are spectacular and not boring at all as there are far too many pretty shiny things to drool over (the Kings Appartments, the Silver Room)! Maybe an audioguide will be better than a guided tour as you can move at your own pace.
2.
Gruesome Tour part 1 - visit the
Kaisergruft (or
Kapuzinergruft at Tegetthoffstr. 2, two blocks behind the Opera towards St Stefans, just past the Memorial Against War and Facism), last resting place of the bodies of the Habsburgs; only their tombs are visible, so not too grim, but interesting nonetheless. Their hearts are kept in St Augustin church around the corner, but you need arrange a visit.
3.
Spanische Reitschule or the Lipizzaner riding school - you've probably already earmarked it, but check
www.spanische-reitschule.com/ and plug in the dates you'll be in Vienna to see what going on in terms of performances or tours (they take a break for part of Summer). If you're there for morning practise, grab tickets. I first went when I was 17 and loved it, have been again twice since, so might be worth considering. The musuem attached isn't half as good as seeing the real thing in action.
4.
Gruesome Tour part 2: the crypt (catacombes) under St Stefans (St Stephen's) church; there are short guided tours of this rather interesting part of the church. There used to be one that also encompassed climbing the bell tower. The crypt
5.
Bakery tour - do what the Austrians (and Germans) to and at 4pm have "
Kaffee und Kuchen" (coffee and cake). Grab a strudel, Sachertorte or whatever takes your fancy at Demel (at 14 Kohlmarkt), sit down in the gorgeous cafe on St Stefansplatz next to the church, or try Cafe Diglas (Wollzeile 10, near Stephansplatz) and enjoy a strong Austrian coffee (Kaisermelange is with milk if you don't like your spoon standing up in your coffee!). If you really want to spoil yourselves, go the whole hog at Cafe Sacher (on the side of the Hotel Sacher) and have Sachertorte with cream and strawberries. This is the home of Sachertorte, and it's kind of cool to have it there, but good Sachetorte can be found around the city.
6.
Go to the Zoo! - referred to as the oldest zoo (
Tiergarten) in Europe, it's located in the gardens of Schoenbrunn Palace and whilse it's not huge, it's a pretty stroll through the animals (if you like zoos). Once you've done that, wander up the hill behind the palace for a great panorama of the city.
7.
Horse and Carriage rides - if you feel like seeing the city from a different angle. They might be a tinsey bit touristy (ya think!), but naff as they are, it's a nice way to see the sights for a little bit and rest your feet.
I'm sure you have your own list of sights to see
WT, but at least these will help convince your daughter that Vienna is worth the visit. Either that or you can trade one from our list of things to do for each one you visit off your list!
Herrbert's restaurant recommendation (Restaurant Gutenberg) is a good one, and although the schnitzel at
Figlmueller are flat they are huuuuuge. Worth going to just to see it hang over the plate! Some other food recommendations are
Café Restaurant Landtmann (Dr-Karl-Lueger-Ring 4) where Freud reportedly took his morning coffee in this old-style Viennese cafe;
Restaurant Beisl is an old Jewish restaurant and Vienna favourite; for something other than schnitzel, try
Drei Husaren (Weihburggasse 4) or
Plachutta (Wollzeile 38), both have good Austro-Hungarian food and a specialty of Tafelspitz (broiled beef with apple and horseradish sauce).
Hmmm, wonder where I can get a quick strudel right now! ;D