Oh, Budapest, Budapest, Budapest! How I wish I could join you Anne and once again see Buda of the hills and bustling Pest.
A first suggestion; seeing as you are coming from Vienna, a city well known for its coffee houses, perhaps you might conduct your own personal survey. Compare the Budapest coffeehouses with those of Vienna. I think you'll be pleasantly surprised. We found that both the quality of the coffee and the pastries easily rival or surpass those of Vienna. Plus the service (by young women instead of the more staid and unapproachable Obers) was more convivial while the cost was a fraction of that in Vienna. That said here are my suggestions for coffee houses to visit (I suggest midmorning and late afternoon visits):
1. Ruszwurm at I Szentháromság utca 7. In the Castle District (Buda side)very close to Matthias Church. Memorable sour cherry/cream cheese strudel & raspberry torte. We arrived early in the morning just as they opened. I've heard it gets very busy.
2. Angelika at I Batthyány tér 7. Down along the waterfront of the Danube, also on the Buda side. This large rambling café was the favorite amongst the literati at the turn-of-the-century. Reputedly a number of plots to bring down the Habsburg Empire were hatched in its dark alcoves.
3. Muvész at VI Andrássy út 37. Across this tree-lined main boulevard from the Opera House sits this great café where you can relax at a sidewalk table and watch the people pass by. My wife loved the Ischler (strawberry-jam filled cookies iced with chocolate) while I tried the ice cream.
4. Jegebufe at Deák tér. A commuters café. The Jegebufe is located above the junction for several of the metros. People scurry in and out as they make their way to work or home. An interesting contrast to the more relaxed laid-back cafés listed above. This one reminded me of the stand-up espresso bars one finds in Venice. But they still have fantastic pastries.
You'll notice the absence of Gerbeaud, arguably the most famous of Budapest's coffeehouses. Although we passed by it a couple of times we'd already enjoyed these other jewels. And as it turned out we were able to experience its pretentiousness at the cafés in Vienna.
Well, Anne, I realize this might be a bit specific but it definitely is one of the charms of Budapest. I've got a portion of our travelogue which I'll put on the shared files area of the website. Here is a website which should be helpful http://www.fsz.bme.hu/hungary/budapest/budapest.html
I've got plenty of other suggestions if you'd like.
John Rule San Diego, CA http://sites.netscape.net/flowsdad/homepage/mtc.htm