There are a LOT of fun places in Nassau where you won't get hassled. Atlantis is definitely one of them. Cabbage Beach is also really nice. There's a Margaritaville and a Senor Frogs there, too. The Queen's staircase isn't as nice as it was when the Governor's Hotel was still there, but it is interesting. When we were there last year, we negotiated with a cab driver who took us to a few areas of interest then to Atlantis. He got us into areas of the aquarium we probably weren't supposed to be in, but no one hassled us. The aquarium is magnificent and the grounds are amazing. It's well worth a $4 cab ride.
The locals can be aggressive, but they're just trying to make a living. It's a foreign country, so they're not governed the way the US is. Just be aware of your surroundings and you'll be fine.