Keys would be great to start. Consider the middle keys as well. Better reefs closer in that Key Largo. Forget Key West for now.
Best in my opinion is Bonaire. Shore diving freedom, great vis and reef. Many folks rave about Bonaire as their first intro to OW diving and love it tremendously.
Belize is also fantastic with varied opportunities for newbies.
Bahamas can be great as well, particularly if you get away from Freeport and Nassau but those can be decent as well. Better reefs elsewhere.
Utila in the Bay Islands of Honduras is wonderful, particulalry for Whale Sharks.
Cayman's is good as well - might try Little Cayman or Cayman Brac even.
Turks and Caicos is fantastic to start your diving career.
Great Barrier Reef is only good (having been there) if you get out and away on a live aboard. But if you are going to the Pacific then French Polynesia, Thailand, Indonesia, Truk (Chukk), Palau, all are great diving. Many others too numerous to name. The Maldives is an option. The Red Sea is possible as well - great dive reports from there. Hawaii is good diving but not reef kind of stuff. Fantastic turtles in Hawaii and the chance to see Manta Rays.
Whereever it is - have fun.