I know only where I've dived, and in 15 years I've not dived outside the US (boo hoo, I know, but I've had fun). And maybe you have an air travel-passport trip in your heart, so I wouldn't try to dissuade you.
Where I have been is offshore Texas and Florida, both Panhandle and East coast around West Palm and Jupiter (and New England, but I will guess you want something warmer).
the Texas Flower Gardens are a fun, inexpensive, no-frills liveaboard experience, out of Freeport. Not much to do ashore, but Houston and Galveston are close. Not exactly a newbie dive venue, far offshore, but in September with fair weather it's warm, and if the current's light and they match you up with a good buddy, the water's real clear and it's pretty coral diving. I did it as my first post-cert dive trip, and it was great.
Florida panhandle is more a regional than a national or international dive mecca, but it's good--wrecks and a little coral, and a fun scene on shore with Pensacola, Destin, Panama City Beach. The "inshore" wrecks are good diving, little to no current, doable for a new diver.
Florida east coast where I've been, West Palm is good, variety of boats and levels of challenge, and a nice introduction to drift diving. The Jupiter scene a bit more advanced and spearfishy, so you could try West Palm, several good ops and lots to do ashore. And I haven't done it but the Florida Keys have shallower coral and I understand much of it is good for new divers, and beautiful. And you have Miami and the Keys.
So anyway, best of luck where ever you go.
