Distant travel destinations often take a couple of days to get to and from. If you're out 4 days of a week's vacation, and the torment & expense of the travel, that's a bad trade off in my book. You're U.S.-based, like me. I've been no farther diving than the Caribbean (Bonaire), and I'd plan to take 2 weeks off for a trip to, oh, say, Komodo, Palau, the Philippines, etc...
If that $3,000 includes airfare, I think you're written off some of the far distant destinations. I take solo dive trips from time to time, and I tend to budget maybe $3,500 - $4,000 or so?
You're to the far northern U.S., pretty centrally located. Check your airfare for varied destinations; after Cozumel, some of the main 1st tier destinations include Key Largo/Florida Keys (you've been), Roatan (e.g.: CocoView, Anthony's Key Resort - which is where I think ScubaBoard is doing an Invasion trip next year?), Bonaire (love it; famous for independent shore diving; I recommend going with a group your 1st time to learn how it all works, including getting around on land) and Belize (which has a lot of options; to narrow it down, consider Ambergris Caye vs. a live-aboard trip).
Not sure where you'd do warm water diving & take surfing lessons; somewhere in Florida maybe? Divers bobbing at the surface & trying to get back on dive boats don't like big waves.
Here's my trip report from a live-board trip May 2015 out of Belize (the boat's been renamed the Belize Aggressor IV). We've got a thread,
Picking a Caribbean Live-aboard. The Caribbean Explorer diving St. Kitts and Saba tends to be cheaper than some other options.
If you really want cheap and don't mind roughing it, check out
T.C.'s 2014 trip report from a Blackbeard's cruise.
If you want some cheap dive trip options, with costs discussed, check out
Total Cost Mid-range Budget Florida & Caribbean Trips.
Richard.