The Abacos are good but shallow. You should be pretty OK with a 5'5" draft but we had places we wouldn't be able to visit with our 6' draft.
If I was going to leave a boat for extended periods of time I'd probably look at the Nassau Harbour Club (obviously in Nassau). Cheap fares in and out from tons of locations - many direct. Lots of services - ships stores, full size grocery stores, etc. to outfit from. There's a great grocery store right across the street from the Harbour Club (and a Dairy Queen!!). You are less than a day away from the Exumas AND a day away from Spanish Wells/Eleuthera.
Yes, Nassau has a lot of crime but it is GENERALLY not perpetrated against non-natives. All of the marinas have full time security and are locked up at night. Unlike many people, we actually enjoyed Nassau. There are numerous things to do, and if you don't feel like going out sailing you can catch a movie, eat at one of the numerous restaurants, spend under $5 and take a jitney "tour" of the island or go over to Potter's Cay and get a great conch salad from one of the 20+ shacks. And when you want to be away from it all, untie the lines and later that day you're at Allens Cay.
Just my two cents...