Being a travel agent, I can give you some advice.
Atlantis is a awesome resort. You are probably though looking to spend about 300 per night and up depending on when you go.
Paradise Island is the best part of the Bahamas in my opinion. You can stay at Comfort Suites which is right down the street, and use full facilities at the Atlantis. You can get a room there for about 150 and up per night.
Downtown Nassau is horrible in my opinion. You will get hassled for weed, and at the straw market. They sell lots of junk there.
Some good buys for vacations in my opinion would be in the Playacar(Riviera Maya) are of Mexico, sometimes you can go All Inclusive(flight, meal, drinks, tips) there for a week for about 1000 per person, they have some nice resorts like Iberostar and Secrets.
Another Nice Island but a little more pricier would be Aruba. Divi is nice right on the beach all inclusive usually around 1500 per person for a week. People won't hassle you there either.