We went during Christmas week in 2014. It was shortly after Dolphin Tales 2 came out so it was madness and mayhem. Plus, some of the movie stars were visiting for photo opps that day. We made sure we got there about 15-30 mins before opening and everything went super smoothly. like everywhere else, the first 1-2 hours was not particularly crowded. We returned later in the afternoon to poke around some more and heard people say they waited 3 hours in line to buy tickets. The line to buy tickets was STILL insanely long, and this was getting closer to closing! my guess is that once you promise to take your kids to visit Winter, you will stand in that line come hell or high water.
During the busy season, do your best to get there early. It was so busy in the afternoon that there were lineups to go up and down the stairs. Oh and DON'T bring strollers. There are stairs everywhere and strollers are a pain. The aisles can be narrow and it is just easier without strollers. For us, we're very comfortable dealing with crowds and even the afternoon mayhem didn't bother us. We still found some quiet spots and it was in the afternoon that we patiently waited a few minutes for an underwater viewing spot and watched Winter swim (amazing!). We also saw nobody near another underwater viewing spot at Nicholas' tank. We waved a popcorn bag around (a trick someone on the Dis mentioned) and sure enough, Nicholas came over to check us out. It was amazing being face to face with him! He spent quite a few minutes with us

And even though the place was jam packed, nobody came over to see what we were doing since it was a small window.
Also, the Little Toot boat ride was the most exhilarating thing our family has ever done. Amazing - especially from a quick little boat like that! I personally didn't think it was overly expensive, especially for what you get. Last year we were in Cali (for DLR of course) and did whale watching from one of the bigger boats. It was very cool, especially since a group of whales hung out in the same spot for over an hour PLUS we saw a pod of 50+ dolphins swim past our boat, but it was not the same as having dolphins leaping and jumping within touching distance.
The drive is easy - just avoid Tampa during rush hour. We went at the end of our WDW trip and flew home from Tampa.