I spent a week backpacking around Romania late last year, it was awesome. But Bucharest was the lamest thing about it.
The most interesting thing the city has to offer is the Parliamentary Palace, and a hideous testament to the abilities of communist goverments to build shit that's bigger than it needs to be. It's one of the biggest buildings in the world. I tired to take a tour but there was some kind of summit happening that day so they refused to admit tourist rabble like myself.
The wild dogs cover most of the country because the commies levelled all the houses they and their owners lived in, and built enormous apartment blocks instead. Hence, homeless doggies. Some are really nice, some can be a bit scary, most are totally submissive but sometimes one might follow you around a bit. The real issue is the Gypsys and the taxi drivers. Hide your wallet somewhere that small Gypsy kids can't reach it, they run Oliver Twist style pickpocketing operations. Seriously. The locals hate them with all their might, and they're the dodgiest fuckers on the planet. I had some old guy with a goiter-esque growth on his arm the size an apple beg me for money, even though he had gold teeth. FUCK gold teeth!
Taxi drivers are the only real way to get around the city, but will fleece you for everything you own, spit on you, and denounce everything you believe in if you give them a chance. They're the real vampires in Romania. You shouldn't pay much more than about one Ron per kilometer or so, but I had one dude that acted like he was my best friend until I got to the destination and realised he'd fixed the meter so he charged me seven times what he should have. And it was a really, really long ride. Make sure you sit in the front, check what their meter is charging you, and don't be afraid to tell them to pull over if you think they're ripping you off. Better yet, for longer trips, settle the total before you leave. I got some good deals on quick cross country taxi rides at decent prices like that. Drivers in the countryside are much nicer. If you find a good one, take his phone number.
Having said that, the currency is retarded. 1 New Ron (also calle a Lei) is also worth 10000 Old Ron, and 100 Bani. Whatever, look into it online.
Dracula's Castle is pretty sweet, it's near a town called Brasov which is fifty thousand times cooler than Bucharest, and it's a relatively short train ride from there. It's settled in a valley and has awesome Hollywood-style signage on the hillside. The castle has virtually zero connection to any historical basis for Dracula (the real Vlad the Impaler's castle is in ruins, it's called Poeinari Citadel. It's on a hilltop in the southern end of the Transylvanian Alps near an absolutely beautiful town called Curtea de Arges) but it's still worth visiting, as is another nearby castle called Raznov.
If you can be arsed, take a trip up to a town called Sighisoara. It's the loveliest place I went to. It's a bit of a trek from Bucharest, but if you've got time it's worth it. Brasov is on the way, and it'll also give you a chance to get into the mountains, which has the most incredible countryside. It's kinda like something out of Lord of the Rings in places, I loved it.
I hope I didn't make Bucharest sound totally shit. There's some really nice areas hidden away, you just have to be willing to investigate. I had a Lonely Planet guide that was pretty handy for directions and tourist ideas, but totally fucking useless as far as advice on hotels and hostels.
And Martin Savage is right, there's some total foxes running around. I was making out with one girl who bit my lip so hard I wanted to cry. Cry semen out of my willy, that is.