I really like Budapest, and it doesn't feel touristy (there are tourists, but they're concentrated in just a few places, and the city is large enough to absorb them). You can "hit the highlights" in 2-3 days, but of course more time will be more relaxing. It's worth a trip for the food alone. For historical museums, there are two that you'll want to see. The House of Terror is about the Nazi and communist periods (parts are as grim and depressing as the name implies, so be prepared). And Memento Park, while out of the center and so somewhat hard to reach, has the communist era statues (Lenin, the glorious proletariat, etc) that other places got rid of after the fall of the Iron Curtain, but Budapest kept.
The other towns in Hungary that I've seen are Szentendre and Vac as separate daytrips from Budapest, and Eger and Pecs as separate overnights from Budapest. I liked Szentendre, but it is indeed very touristy. I loved Vac and had it to myself (the other tourists are missing out). I didn't like Eger (although it was raining for much of my time there). I liked Pecs a lot, and could have spent an extra day; again, at least in 2008, there were few tourists. I found Pecs and Vac in Frommers Budapest; at the time, neither was in Rick's Budapest book, although Pecs is now.
I haven't been to Sopron, but it's right near the Austrian border, can easily be seen between Vienna and Budapest (although not on the most direct route between them) and sounds interesting. It's also covered in Rick's Budapest book.
Sorry, I don't have any information about your main question, as the only place I've been in Austria is Vienna.