In Budapest, try slovak sorozo, located on the North end of the Pest side. Combination slovakian and Hungarian, it's delicious. Just ask the waiter for his recommendations, and you'll be fine. In Vienna, my favorite was Immervoll, a traditional Austrian gastro-haus.

Also, if you're a wine drinker, you'll really enjoy the high quality and low priced wines in Hungary, especially the reds. In Austria, I'd go for the gurner veltliners, which are typically served as house wines there, which is a hoot for anyone who's paid (as I have) $10-12 for a nice glass of GV).