Budapest... hmmm, just don't eat/buy anything from the main shopping street Vaci Uca. I know ht's a very typical tourist trap, or so I think. But if you keep wander down south of that street, there are a few locals places there. Sorry but it's been years, and I have long forgot the names of the joint. As far as places to see, try to walk around the river and visit the roman spas. It will be a lot of walking for sure, but you will love it. I'd say from the south, you can start at the Elizabeth bridge and walk north towards margaret Island, and cross the river and make it a circle if you are interested in a 10km walk and get all the sights in.

of course, there's the beautiful andrassy avenue, the heros palace, and the winter palace that used to be the worlds fairs ground. In those cases, I'd advise you to take the metro to get there and shave some time off.

As for vienna, you should rent a bike (1 euro/hour) and ride it across the river into the new town. It's a drastic change, but you also get to ride pass the UN europe headquarters. Get on top of the A1 tower, never been there but I heard the view is nice! As far as old town goes, everything is within walking distance, so, just follow the map and you will be fine. Eating wise, definetly try the wienschnitzel, and the lean steak (dont remember the name), it's very different from the greasy meat you are used to in the States, oh, and try their potato salads.

Last, but not least, Demel cafe, and Sacher hotel. probably the two most well known bakeries there. Personally, I really love the black forest cake in Demel, and as for the famous Sacher Torte.. YMMV. I liked it the first time, but when I went back years later for 2nd, it was only ok... maybe my taste buds changed?