Jo,
My opinion:
From reading some of your posts, you seem like an adventurous person. I would recommend Mexico as a first choice. Now there are several resort areas in Mexico (I have visited 5 different areas) but if looking for a nice white sand beach I would recommend Cancun, Playa del Carmen or Cozumel. Cozumel (being an island) does not offer as many "off-property"excursions unless you are willing to ferry to the main land. About 45 minutes on the ferry (sometimes a little rough, sometimes not). The ferries have really improved in the last decade. They do offer a nice national park though to scuba dive or snorkel. Also, very limited mayan ruins. The only town, San Miguel, is very interesting to poke around in and I have found prices less here then the mainland. Offer the typical booze cruises and jeep trips etc etc if that is your sort of thing.
The Mayan Riviera offers top rate hotels, amazing food, incredible beaches, and tons of activities and excursions. The Mayan ruins that you take an all day excursion to (from here or Cancun) are unsurpassed IMO. This is by far my favourite area of Mexico. I am dying to get back (its been 2 years since my last visit there).
If looking for something more geared to nightlife and shopping consider Cancun. Cancun offers amazing beaches, nightlife and shopping. This resort spot can be a non-stop party (if you want it to be). The clubs are AMAZING.
Also, in Mexico, Acapulco and P. Vallarta. Great places but do not offer nice white sand beaches. P. Vallarta offers an atmosphere that cannot be described. Walking the malecon at night (boardwalk by the ocean downtown) MUST be experienced, but again the beaches are NOT great. I miss P. Vallarta (haven't been there in 12 MONTHS, I want to go back now). Sorry, off topic.
I do not recommend the D.R. Too many people come back with bacterial infections of one sort or another. The beaches of Punta Cana are very nice but for the same $$ you can get to Mexico.
Cuba is beautiful, and if you want a little attention from the locals, this is the spot. Plus the beaches are A+. The food is pretty basic though since they have difficulty importing a lot of variety. You will not find a ton of off property excursions as well but if you are staying for just a week you could probably find enough to do. Nightlife is limited too (except Veradero, a little more nightlife there). Considering your personal security, Cuba is probably your safest bet .
Overall, I recommend Mexico over the D.R. and Cuba. The quality of vacation you receive for your vacation dollars is the best IMO. I feel it is much safer then the D.R. I vacation to these three countries quite frequently please feel to ask me any specifics. I fell much more comfortable discussing Mexico and the Caribbean then WDW. lol.