ok well we have not done it as I have been researching this for weeks now and asked friends that live in Florida this same question. We were told Siesta Key was the best beach it is calm and soft white sand. its gulf side. I was told on the Atlantic side got to Coco beach lots of waves and more sea shells than gulf side. If you have watched the movie Dolphin Tale you can go to Clear water that is were the dolphins Winter and Hope live.
All of this being said we decided the hotels were expensive for what I am doing. 1 night tricking my kids into think we are going on a beach vacation instead of Disney. We decided to stay our first night in Ocala its only an hour away from the Atlantic side and find a beach there. the hotels are cheap. we are going to play for the afternoon at the beach then go check into disney. ok so Hotels well clear water its a lot mom and pop. little harder to get info on them. Siesta key is expensive resorts mostly. Sarasota has La Quinta and Best western for about 120 a night and its right by siesta key. Now I did find a Disney Vacation CLub resort on the Atlantic side called Vero Beach the rooms ar around 200 a night. I hope all this helps a little.