If you are going in January you won' have to worry about "spring breakers" so that won't be an issue. Also, almost every island has beaches you can relax on so you really haven't given us any information to help you narrow down your search.

Without knowing your budget it's difficult to make specific recommendations. Can you at least give us a range of how much you are comfortable spending?

You should know, single travelers, both men and women, are fairly common in the caribbean so your situation is not all that unique.

Your best bet is to choose an island that you'd like to visit then pick a resort or hotel on that island that will fit your budget. Start by doing some basic research. Use the "Destinations" link at the top of this page, click through to the Caribbean and read the summaries of each island. Choose one or two that most appeal to you and start researching hotels/resorts. Don't let the number of destinations confuse you - very few of the contributors on this forum have visited them all. One island is not necessarily better than the other they are just different islands. That's the beauty of the Caribbean, you can visit a different island every year for the next 20 years and have 20 very different but thoroughly enjoyable experiences. Every island is different and no one island "has it all".

If this is your first trip to the region you'll probably be better off going to one of the more well know islands as they will have the greatest variety of things to see and do. You can save the lesser known ones for future trips.

For starters I'd suggest you look at places the Dominican Republic or Jamaica as they have the highest concentration of All Inclusives that are not "party type places". If you'd rather not go All Inclusive look at St. Thomas, St. Martin, Aruba or maybe St. Kitts. See if those peek your interest and then come back to ask specific questions.