Hmm... Lucaya is "ok" for a little, and if you are going that far, perhaps the Berry Islands and Great Harbour might be fun. I am not sure how the marina is doing these days hopefully the pool was cleaned up and reopened.
Old Bahama Bay is where we stop on the way over to the Abacos. It has a great pool and we enjoyed their beach and restaurant on the beach. Cheaper fuel than the Abacos. Make sure you check the Explorer Chart web site fuel and dockage rates where you intend to stay.
The only reason to go to Nassau would be to fuel up or visit Atlantis for a couple of nights on the way to and back from the Exumas. I have a very recent report that Chub Cay is making good progress towards being a (expensive) destination.