I have sailed out of San Juan twice, so I will try to give you some insight. If you are going in Aug. you are probably looking at Carnival Destiny or RCCL Adventure as I think they are the only two doing southern caribbean at that time. I also suggest that you go at least the day before and stay at a hotel as it is much less stressful and enjoyable. I have also done it both ways and staying over was much better. These are two very different ships, in price and activities. It depends on what you are looking for.
Carnival Destiny June 2001 I took this cruise with two teenage grandchildren, girl 18 and boy 16. We flew down the day of the cruise, and had an inside cabin on a lower deck. Carnival cabins are bigger than most cruise lines so we managed ok, had two lower and an upper bunk. I am in the (not-in-the-cabin-much) category so I like the best price and cruising more often. We enjoyed this ship very much. The pool area is good, and there always seemed to be something going on. They do a good itinerary with 4 different ports(one of the only Carnival ships that do). What I remember most is the lively fun feel of the ship. This is a much older ship than Adventure but it seemed to be kept up pretty well. They also have that great pool slide! Food was also good and varied, with a lot of choices between dining room, buffet, or burgers and pizza. The worse memory of this cruise for me was getting on and off the ship, a real hassle and completely disorganized. I hope they have gotten it together a little better by now. I suggest you read all the reader reviews you can find to make a decision.
RCCL Adventure of the Seas May 2004 This was taken with my daughter and is one of my favorite cruises of seven I have taken. These Voyager Class ships do have it all. I had been on one other, Explorer, with grandson, so this time it was with his mother. We flew down the day before(highly recommended) and stayed at the Wyndham Old San Juan,$130 per nt. If you are on the Carnival Destiny, you can walk to the ship from this hotel, but all others leave from international pier and you must taxi. This hotel has just changed to a Sheraton. It is very good for an overnight because you can walk all around Old San Juan, shops, forts, restaurants. It also has a casino and music at night.
There were torrential rains the next day so we stayed at the hotel until about 3pm before getting a taxi to the ship. The hotel let us check out and stored our luggage in a locked room until we were ready to go. These ships do not sail until 10pm so it worked out fine. We missed the welcome buffet on the ship, but got to walk right on, no lines, so it was great! We had an inside cabin on deck 6, very nice, smaller than Carnivals though.
This ship absolutely blows your mind. I'm sure everyone has seen the commercials so I won't go into all details but it truly has something for everyone. I think teenagers would have a really good time on this ship. We enjoyed all the shows, parades, and activities, especially The Quest! Don't miss this, its hilarious. This cruise is also very port-intensive with 5 ports, so if you are looking to see many places this would be it. I think they run two different routes, both with 5 stops on alternate weeks. The food was good both in the dining room and buffet, but my favorite is Johnny Rockets which is on all Voyager class ships. This was the only place my grandson ate on Explorer! The burgers are excellent as are the fries and onion rings. There was no charge at the times I went (June 2002 and May 2004) but from what I have read on these boards, they are now starting to charge. Big mistake for the cruise line, I think, and kind of petty.
We also stayed over one night after the cruise to try that and we loved that too. It was a lot less stressful than hurrying to catch the plane. We booked the Rainforest Tour with the cruiseline and this got us off the ship with no hassle. This tour was just ok, pretty but kind of boring. They drop you at the airport afterward in an area for cruise passenger luggage. We collected our luggage and grabbed a cab to the Wyndham Condado Plaza. This is a beautiful hotel, it has pools, restaurants(expensive but good) a casino and a small beach,$160nt. By doing this, we were able to relax overnight and take an early flight home the next morning, which is why we decided to try it.
This is a very long message so I'm going to stop. I hope this is helpful to you in making a decision. As I said, read as many reviews as you can and pick accordingly. You didn't say if this was a first cruise or not, but I loved both of these for different reasons. Have a great time!