If you are planning on sightseeing or taking an excursion at a destination port where your cruise docks, make sure you consider the amount of time the ship will be there. Cruises are usually on a schedule and only stay at certain ports for a limited time (different times for each port). You do not have to get off the ship when they dock, after all the food is still available to you at no charge. Your teen however will not understand that because all they are thinking about is having fun. Getting off at the port of call is both fun and educational. Your teens can learn more and get an adventure in return. Keep in mind that you are responsible for your food if you get off and it could be expensive depending on where you are. Make sure you budget for it. You can take from 2 to 10+ days cruise going anywhere from the Bahamas, Caribbean, Europe, Mexico, Hawaii, Alaska, Transatlantic, or a trip to nowhere. Wherever you choose, remember a cruise is a great experience for you and you're teen/ Family.                                        
Caribbean cruises are fun and a popular destination year-Round. September through December is the slowest times and you can get better deals during this time. Unfortunately, your teens are back in school. If you don't mind them missing a week in school, go for it. Spring break is a great time to take a cruise with teens, but you will find that the prices are usually higher during this time. June through November is Hurricane season, but don't let the hurricane season scare you off from taking a cruise. Cruise ships gets plenty of warning if a Hurricane is forming which is rare and can change course if needed. 
Summer is when most families plan vacations so book your cruise early and enjoy.