You are going to have a great time. I have cruised both of these island chains before and they are both great destinations. My favorite is the Exumas.
Pick up a copy of the
Yachtsman's Guide to the Bahamas there is a wealth of information in that book including some tips on where to find reefs. It is the bible of Cruising the Bahamas. I would not cruise without it. It probably has info on islands with air as it has lots of info on where to eat, where to dock and intesting details on the islands.
You will probably come back a good freediver because there are not alot of places to get your tanks filled. We would strictly freedive so I never scouted out which islands have air.
For the Berry's you might want to check Great Stirrup Cay and Chub Cay. Those are the most likely islands that would have air. Between the Berrys and the Exumas is New Providence Island (everyone calls it Nassau) and you can find air there.
There are over 350 islands in the Exuma chain and most are uninhabited. The Exumas are awesome. For air you might check Staniel Cay, possibly Highbourne Cay and Georetown. Georgetown should have air but it would not surprise me if Staniel and Highbourne do not. If you send ONESPEED a PM he should be able to tell you if Staniel has air... he travels there every now and then. It's been over 10 years since I was there.
In the Berry's be sure you stop at Hoffmans Cay and check out the Blue Hole. It is amazing!
You can't cruise the Exumas without visiting Staniel Cay and Thunderball Cave. It's best to visit Thunderball Cave at high tide if you get the choice.
Here is a picture of the Blue Hole at Hoffmans Cay:
Here is the entrance to Thunderball Cave:
Hope this helps.
-Chris