I have just returned from Nassau with my husband and 16 month old daughter. Despite some setbacks (like upset stomachs on the flight down and the baby deciding that she's going to enter the terrible twos 8 months early) we still enjoyed ourselves.
We flew non stop on Spirit from LaGuardia. We didn't have reservations anywhere so we had to park at Dollar. They only had covered parking so it was more expensive, $19/day. However, both going and returning, the shuttle bus was very quick in arriving. No complaints.

Spirit was fine and we got an excellent fare ( $183 r/t including taxes). I did wish they had some inflight entertainment since 2 1/2 hours feels longer without it.
We traded our week through II to stay at the Paradise Island Beach Club. I believe it only has 44 units and they are all 2 br. We had #29, which is scheduled to be redone in 2007. It was very well equipped, especially the kitchen. If I wanted to cook or bake or bbq, I could have. There was a cocktail party with snacks on Saturday night that was free. They also have a shuttle over to the water taxi to Nassau which takes you to by the Straw Market. Note though that there are ground floor units but if you are mobility limited, make sure you get one since we had to go up 2 flights of stairs to get to our unit. My daughter is still small enough for us to carry no problem.

Cabbage Beach is gorgeous. Definately on my list of the top 10 I've been to in the world.

Costs- Taxi fare added up quickly. We wished we'd rented a car like we usually do but for some reason we didn't on this trip. Taxi to the hotel was $50 ( since the baby unexpectedly threw up in the cab, we wanted to give the driver a big tip even so we cleaned it up and he didn't seem to upset since he's got lots of grandkids). It was $6 for a taxi just down to either end of the island, which could be walked.
Food- We ate at Fish Fry. If you don't know it, its an area where there are alot of little restaurants to try that locals and tourists frequent. Our first choice was closed for renovations so we went with Seafood Heaven. I had fried lobster and shrimp and my husband actually got steak. Our tab with 2 drinks for each of us came to $62.
We had lunch at the pool bar at the hotel one day. The grouper sandwich was very good.
The best meal we had, and one of the best we've had on our trips and we eat at nice places when we travel, was at Columbus Tavern at the Marina. My husband had snapper and I had conch chowder that was so good. The conch was not rubbery or tasteless. Desserts were yummy too. The atmosphere is excellent too. Its right on the water and opensided.

We also took a cab over to Cable Beach and had dinner at Johnny Canoe. It was really like a colorful Dennys but we enjoyed it. Nothing special though.

Finally, there is a $50 tax that I believe all hotels charge. We also had to pay a $7 energy surcharge and $2/day for the crib.

This is brief but I hope helpful.