Depends on what kind of entertainment you're looking for.
I typically stay in the 6th and 7th districts and I prefer the "kert" bars (ruined apartment buildings turnt into two level bars - only way to describe them!); however, as summer is here the open air bars and the island will become increasingly more popular.
I wouldn't recommend crossing into Buda unless you're staying there or you really want to visit something specific as public transport can become a nightmare. A38, however, is well worth a visit, but it's right on the river and the 4-6.
The most popular areas for tourists seem to be Raday utca and Liszt Ferenc Ter and while they're deffo nice and you'll feel quite posh and very trendy, they have the price tag attached. They're all more to be seen and to see. Popular bars, in general, include: the famous Szimpla Kert (kert bar) and then Instant and Mumus, the other two quite popular kert bars (I recommend Mumus), you have Holduvar on the island, as well as Cha-Cha-Chad. Romkert is having a real renaissance and so is West Balkan. For a little more upscale and to schmooze, Bar Domby and Boutique Bar are quite groovy. Moulin Rouge and B7 are club atmospheres (but that's not my forte).
If you don't stray from the 6th district and the 7th, you'll be fine. Lots of places to try and explore and always loads of people. Some of the little side streets will be quite dark, but I promise it isn't bad.
Avoid the 8th district and the Blaha Luzja underpass if you do go to Corvinteto. I'd rather battle traffic than anything underneath there! Hope that helps! almost 8 years ago