You are correct about not wanting to head to the Keys. Its not known for it beaches, although there is a nice state park beach there, Bahia Honda, as well as Smathers Beach, which is too narrow and busy to suit me, and it is a very, very, very, very long drive.
You would be pushing it to allow 2 days for a keys side trip to your Disney vacation and as I guesstimate it would be about 12 hours of driving, round trip, at least. We found this out by trying it one day. Yes, my bright idea..."Lets drive down to the Keys!" thinking that we could do it as a day trip from WDW. DH being the good guy he is, tried. Well, many hours later, we wound up in Miami, sick of driving, with a long way still to go. We found some street metered parking and walked through an old park, over a wooden boardwalk/sand dune and saw the most gorgeous turquoise water I have ever laid eyes on. Maybe 2 other couples there on a long stretch of white sand beach.....very nice, but still a long, long drive. We did, soon after, dedicate a vacation to visit the keys and loved it.
I have not been to the Captiva area, but have heard it is awesome.
But for a not too far away beach trip, I suggest that you visit the Clearwater area or on the other coast, Cocca Beach. I have been to and enjoyed those beaches last year, and our kids had a blast.