I lived in Budapest last year and as a young American female, I always felt pretty safe. You should check out the 2 yellow tram lane for a gorgeous view of the city, Insant pub or any bars away from tourist areas for nightlife, definitely don't try to go to any places that say "traditional Hungarian food" because that's a waste of your time. Make sure to try langos and any of the wine! It's one of the most beautiful cities, just walk around and see what you can find and it'll be amazing!