Vienna

Ring Tram - total rip-off; take Tram 1 from Oper to Schwedenplatz (or vice versa) and you'll see the highlights: http://www.wienerlinien.at/media/files/2011/linie1_folder_en_53384.pdf Vienna Card - decide for yourself: http://www.tripadvisor.co.uk/Travel-g190454-c128091/Vienna:Austria:Should.I.Get.The.Vienna.Card.html As for your route, I would suggest the following:
Day 1 - Opera, Kaerntnerstrasse, St. Stephans's, walk around the first district (use self guided walking tour from Frommer's on their website), across the Graben, down Kohlmarkt (have coffee at Demel or Cafe Central), visit Hofburg (don't go inside the apartments as they are very similar to what you will see at Schonbrunn; visit Schatzkammer); Kunsthistoriches (probably not time to go inside); MusuemsQuartier for a drink; dinner at Spittelberg. Day 2 - Naschmarkt; Secession Building; Majolika Haus; cafe Sperl; Schonbrunn; heuriger in Nussdorf for dinner Day 3 - Belvedere; Karlskirche Best place to stay is in the first district.

@ Fred , Many thanks , at my age my eyesight isn't what it used to be ! We're staying at Westbahnhof too and I wanted to make sure I didn't wind up at the Prater Ferris wheel . My best , Steve

Hi, Which area are you staying in? From the Westbahnhof (west train station) area (if you're staying there, which is where I stay), you can get to Schönbrunn directly...take tram #18. stops across the street from the palace.

Fred , do you mean # 58 tram ?

Sorry, you're right. It's Strassenbahn #58 from Westbahnhof to Schönbrunn.

@ Steve...Good choice at Westbahnhof. Numerous hotels, Pensionen, and a few hostels too are in the immediate Westbahnhof area, all depending on your price range, esp in July and August when the rates are at their cheapest. From Westbahnhof are direct trams (Straßenbahnen) to Schönbrunn, Zentral Friedhof (Central Cemetery), and the Army Museum (Heeresgeschichtliches Museum) at the torn down site of Südbahnhof (south train station), plus two U-Bahn lines converge at Westbahnhof.

Personally, I find the Westbahnhof area to be about the ugliest part of Vienna. Maybe you'll find some cheap places to stay, but you'll be surrounded by gentlemen's clubs, heavy traffic and graffiti. Not a place I like to wander around in the evenings. Also, transportation in Vienna is excellent and Westbahnhof is definitely not a hub for local transport within Vienna. If I were coming as a tourist to Vienna and really wanted a pleasant experience, I would stay in the First District, or areas just outside of it. Staying there would essentially eliminate the need to use any public transport at all (except for visiting Schonbrunn).

We have stayed in this area before and I don't think it is that bad. We stayed at the Fuerstenhof and had a great time.
We loved walking down Mariahilferstrasse to City Center. Since then we have rented apartments over in the Augarten area which is not in city center either, however with the excellent public transportation we were in city center within about 5 minutes.

"...I don't think it is that bad." Quite true, otherwise why would the chain hotels (Motel One, Mercure, Ibis, InterCity, etc. be located there at Westbahnhof? True, relative to other tourists, you don't see that many Americans there. Some of the restaurant prices seemed tourist inflated. Take the U-Bahn out to Nußdorfer Straße to get some real cheaper prices, esp for Schnitzel.

Not meaning to make this a pile on . I am making my first trip to Vienna on this occasion but have studied about the city for many years , Also the access to maps and pictures via the internet provides much better information than , say ,twenty or thirty years ago . I'm sure Emily is quite right about the ambience of the old city , but hotel prices increase in all cities as you draw near to dead center . Last fall we stayed near Termini in Rome which seems to get a similar bad rap , but it was nothing like that . Having stayed at numerous Accor properties ( Mercure , et al ) in the last four years ,I have never been unhappy with the quality of the rooms they provide . I have also found that in many cities ,a ten minute ride on a metro or tram can save a lot of money . So , by booking my room at the Mercure Westbahnhof , I saved between $ 100 USD and $ 150 USD per night instead of one of their properties ten minutes away ( Secession , Josefov , Biedermeier , etc ) The hotels I looked at near the Ring were much higher in general . I want a clean , relatively nicely outfitted room , but considering how little time I spend in it , I find the ambience and atmosphere I seek in the places I've come to visit .

I've always stayed where Rick Steves stayed: K&T Boardinghouse. Tina and Kaled are great hosts and now have a second location closeby their original place.
The price and location simply cannot be beat, with the subway and a large supermarket out the front door. Restaurants are all around them. You can be within The Ring in about 4 minutes.