Can’t recommend Bucuresti highly enough. I love the city, though you’ve got to work a little at it. (FWIW, I’ll plug a couple travelogues I wrote that are easily accessible at
http://members.virtualtourist.com/m/27b80/35f/ (much of the country in nine longish parts; scroll down the page).)
I’ve heard a rumor that it’s closed. If not, La Taifas - Strata G. Clemenceau 6 - behind the Athenée Theatre has a couple of small rooms, but they’re always crowded. The menu is written on blackboards and features traditional dishes. A warm, comfortable place that doesn’t take credit cards.
Another favorite is Bistro Ateneu - Strata Episcopiei 3 – close to the Athenee-Hilton and the Atheneum, around forever. Very cozy, reasonable, very popular locally...if you like the environment, this is the place you would want to go. Open late, live music as I recall. (Reservations recommended).
Hanul Maramures, str. General Berthelot 24 (set very far back from the street on the north side--I walked past it about five times without seeing it!), serving traditional food in a comfort-able setting at very reasonable prices
Doina, Soseaua Kiseleff 8 - a pleasant drive and somewhat fancy. A wonderful outdoor terrace and garden and beautiful indoor setting for an excellent, if expensive, meal.
Doi Cocosi, Soseaua Bucuresti-Targoviste 6 - a bit of a distance on the road to Targoviste, is also excellent. Don't let the touristy air throw you. The food is quite authentic. (And you will almost certainly enjoy the show!)
Though some guidebooks recommend it, I didn't care for the Aquarium (str. Alecu Russo 4). It is a beautiful setting in an old villa, but too stuffy for me, too expensive, and a very limited menu. Food was fine but the experience has kept me away ever since. By the way, you can expect excellent traditional Romanian music at all of these places (Doi Cocosi even has a folk dance show). You can safely skip Hanul lui Manuc, an old caravanserai and sadly, Caru cu bere has closed after over a century. I’ve heard that Casa Capsa on Calea Victoriei has re-opened; if so, that’s a very old classic that’s almost certainly worth stopping in.
The one thing I would note is that the restaurant scene is changing all the time; there are some truly excellent places to be found. Nose around.
Sibiu is tough. It’s relatively small and you’ll have trouble spending two full days seeing what there is to be seen. That said, it’s got one of my favorite hotels of all times, the Imparatul Romanilor (the Roman Emperor). The dining room is what you’d expect and I have a hard time recommending anywhere to eat in Sibiu, sad to say. Still, it’s a beautiful Saxon town, worth the visit. Sighisoara, the same. It’s even smaller and, but for the medieval castle on the hill—which is easily worth a few hours of wandering around—there’s little here, including restaurants, unless things have changed substantially since I was there. Sadly, for all my enthusiasm about the country and the people, this shabby town is simply without much charm. The castle is worth every moment, but you won’t find much else.
If your plans should include Brasov (likely), Iasi, or Cluj (both unlikely), let me know. I can easily recommend places in all three. If you planning on shorting Bucuresti, I wouldn’t. I may be overly fond of the city, but I could wander it for days. It’s a fascinating place and, if you don’t have time to see much of the country, I would definitely recommend a visit to the Village Museum (Muzeul Satului). They had a disastrous fire about five years ago, but it is an exceptional open-air museum with examples of architecture and homes from around the country. Absolutely fascinating.
Budapest.
Kispipa Vendeglo - wonderful Kispipa ('Little Pipe'). A small, out of the way restaurant serving mostly locals. Not fancy in the least and not very expensive. Our waitress spoke very little English but it didn't matter. We had a wonderful time ordering, watching other diners, and enjoying a truly great dinner. (Skip its sister place, whose name escapes me but has nowhere near the quality of food.)
Gerbeaud’s - A pastry shop but oh what a pastry shop! It's a classic and every guidebook recommends it. So do I. It is readily accessible on Vörösmarty ter, at the end of Vaci utca (the main shopping street for tourists). It has a 'blue-haired old lady' feeling to it, but it's also irresistible. Fancy, very classy--even if the serving ladies aren't exactly friendly. Try the Hungarian classic, Dobos torte, with coffee. Or if there is something else that strikes your fancy, go for it! The selection is enormous, the food very good, and the prices even reasonable. What more could you want? (They even have tables outdoors for those days when you just have to sit outside.)
Also the New York Café, if you have plenty of time but a desire to visit one of the classic turn-of-the-century cafes. Fabulous architecture. Budapest IMHO, suffers from an overabundance of middling quality places. The truly worthwhile places are hard to snuff out—at least they eluded me for the most part.
Prague.
I won’t add to what everyone who’s ever visited has no doubt told you. It’s fabulous. I’ll limit my recs to two: U Maltézských Rytírù (and some of the accents are missing because I can't reproduce them!--You should have heard me trying to pronounce it when I asked for directions!)(it means, 'At the sign of the Maltese Knights'): a wine cellar with niches carved into the walls where tables are set. Wonderful atmosphere. Very good food. A very nice experience and a great introduction to the city. U Matouse (At [the sign of] Matthew's [house]). This is a real neighborhood place that most tourists will never find, wonderful 'real' Czech food, very reasonable prices. But practice your Czech--no one spoke more than a few words of English (and no French and no German the night we were there!). The dinner was excellent, but even better was the experience of discovering it and being tourists in a place that rarely (if ever) sees them. Another, in a cellar, eludes me—but this is a place you will find it hard to have a bad meal. I never did.
Gypsy Boy
"I am not a glutton--I am an explorer of food." (Erma Bombeck)