Destin has quickly become one of my favorite vacation spots. I have been twice now, once on my honeymoon and once on a family trip. Each time we go is just as enjoyable as the first. From all of the activities and dining places, not to mention shopping, you are guaranteed to have an excellent time with or without kids. Make sure you grab one of the entertainment/guide free books in the lobby of your hotel, as they will have several coupons and discounts to area attractions and dining.
One thing to definitely explore is the Southern Star dolphin cruises. You are guaranteed to see dolphins, and these cruises are very laid-back and a good time. They are also inexpensive! I do recommend making reservations ahead of time, as the cruises can fill up quickly. We also took a jet ski tour that was an early morning excursion. We left at 8am and it was a 2-hour tour. Several companies offer different tours, so check around for the best price. We did one of these tours and saw so many dolphins some close enough to touch, although you cannot bother them. This was a great time for us, and if you really want to ride a jet ski, this is the way to go. You have a guide, so you are not limited on where you can go. The vendors set up right on the ocean tend to be a bit expensive, and your boundaries are so close, it's not worth the money.
If you have kids with you, you may want to spend a day at Big Kahuna's water park. Although we've done this twice, it is a fun time but is a little pricey, so make sure you have a full day to spend, as lines can be long in peak season.
If it is food you are seeking, Destin has some great choices for food. My personal favorite is Fudpucker's. I would suggest going in either late afternoon or around lunch time, as the wait can get very long. While you wait, you can look down at the alligator pit ,where they have roaming alligators just hanging out for people to view. You can also purchase food and feed them, which always stirs up excitement. At certain times they have a baby alligator for the kiddos or adults. You can take a picture while holding this alligator (moms, don't worry , the mouth is taped shut and it's very gentle). This is a great memento to have.
Joe's Crab Shack also has a family-friendly atmosphere that kids and parents alike will be sure to enjoy. While you take in the great food and awesome decor, don't be shocked when the wait staff breaks out in song and dance right there around all the tables. I high recommend this place.
If you are looking for something a little more low-key, you can try AJ's. The wait here is long as well, but it has a stunning view of the harbor and can be quite romantic, but it good for families, too. They have great food and are a little pricier than some of the places, but it is well worth it. And you can't leave out the shopping. Destin has a wonderful outlet mall with some great name-brand shops where you can find excellent deals throughout the year. This is perfect for that rainy hour of the afternoon that always seems to pop up...