WB, I'm going to guess you are located in the SE USA (you mention cruising in the Caribbean). If that's correct and if you don't mind leaving your boat on the hook (which is likely the only affordable way you can approach this idea, given the air fares will be costly enough) then IMO the key is to choose the right anchorages
. Here's one set of examples you can consider:
down to G'town, Great Exuma (post storm season): leave the boat in one of the 'pools' and under the care of one of the regular Bahamian caretakers down there who is recommended by the cruisers; this isn't all that unusual an arrangement (tho' getting a spot in one of the pools is easier if you arrive before the gaggle of Snow Birds). This allows you time to visit some of the Bahamian island groups and reach G'town. Flight back via Nassau
G'town to Luperon, where you'll anchor
in the big estuary: Not a place I like to recommend for a mix of reasons but it will have long-term boats and finding a caretaker won't be hard; safer than Manzanillo and certainly more affordable than the new marina in Puerto Plata. Allows sufficient time for visiting a mix of Bahamian islands SE of G'town plus Turks & Caicos before arriving DR. Flight out of Puerto Plata.
Luperon to Salinas, PR: Another fetid, semi-protected but popular estuary like Luperon that you can easily reach in the month period you mention, and again where you can find yachties to look after your boat (if not the marina folks themselves). PR is a far better cruising destination
in its own right than most Americans appreciate. Flight out of San Juan
after a taxi ride over the mountains.
Salinas to Simpson Bay, St. Martin: yet another fetid estuary with lots of semi-resident boats but this time with multiple chandlers nearby should you need to do some repairs/add a system or two. This island has lots of flights and the French side is very casual about length of stay tho' you may need to deal with the Dutch folks if flying out/back in.
You get the idea. I'm not keen on leaving my boat on her own in a foreign port and on the hook, nor in trusting folks that will have access to her, which is what I think is the main wrinkle in your plans vs. costs, logisitscs, etc. With each of these 'jumps', there are marina alternatives in the same area where the boat would arguably be much safer BUT which will be relatively more costly and not help you pay off the college debt as easily.
In your shoes, I'd look at the SE USA area as my cruising venue instead. The St. Johns River and GA Sounds (including lovely Cumberland Is.) would make one great venue for a month's cruising, operating out of the Indian R. area would allow you to hop over to the Abacos on another segment, the Keys & Everglades would offer some interesting stops for you during another round, then there's the lovely Charlotte Bay (much of it undeveloped) and the beautiful waterfront venue of St. Petersburg for another segment. All of these areas make for good cruising and, with the exception of the jump over to the Abacos, are somewhat independent of weather
since protected waters are nearby - an important consideration given you'll be watching the calendar. However, the 'leave her on the hook' vs. 'cost of a berth' will still be a hurdle you'll have to seriously think through at the end of each cruising segment.