I've been to Budapest with my girlfriend and felt safe there so I think Budapest is safer for any tourists. There are of course some common tourist traps, just like in any other of the European cities. The number one tourist trap in Budapest are taxi scams. Most are legit but others will try to rip you off. Travel only with a taxi that has a yellow license plate and a taxi sign fixed to the roof of the cab and on the side door, otherwise don't use them. There are pick pocketers in operation in crowded places so keep your valuables in a belt bag at the front of your body or in an inside pocket, never on your back or back pockets.
As in most Eastern European cities there are pick pocketing types on public transit, but if you keep your wits about you it's nothing to worry about. Budapest is very safe for female travelers, and the city tends to quiet down considerably at night so there is little street crime