For me, best overall "short relaxing break": Anguilla, Antigua, BVI, Caymans. As PPs have said, don't underestimate the impact of flight times and connections on a one week trip - if faced with equally attractive options, I'd pick the one that gives you the easiest, shortest, and least complicated trip there and back.
Best relaxing with a chance to get out into nature if you don't mind driving a bit: Dominica, St. Lucia, and - BVI again! - Tortola. If you don't mind splitting your time, perhaps some in Tortola and the rest somewhere like Virgin Gorda or Jost Van Dyke.
If you want to maximise the chances for great weather, spend a lot of time at the beach, and maybe get out on the water and do some (easy non-expert - although there are good options too if you ARE expert) water sports, Aruba-Bonaire-Curaçao are a good fit and often very good value for money.
I've spent time in the DR and liked it, but I think can take some advanced planning (and/or maybe some Spanish language skills) to get away from the kind of isolated all-inclusive resorts and the corporate/state travel "feel". Possibly not the best for relaxing for just one week!