The timeshare condos as some have suggested are really nice. We've done many stays at the Sheraton Vistana Resort and it's been a while, but have done some of the other Marriott timeshares too (They always get great reviews) Any of the timeshares will offer more space, balconies or nice patios (something I really like that suite hotels don't offer), and have a great resort feel with more amenities than resort hotels. The Hilton Grand Vacation Club SeaWorld is another nice timeshare we have stayed at on top of the ones already mentioned that is even walking distance to SeaWorld. Also, closer to Universal, we have stayed at the Sunshine resort (another very nice timeshare condo). The timeshare condos IMHO are going to feel more luxurious than suite hotels and are super spacious -- really great option if you are traveling with a large group of people. The best deals on these that I have found is when I do a Fri. - Fri., Sat. - Sat., or Sun. - Sun. rental from a timeshare owner on sites like Redweek.com or TUG2.net classified ads section. Most do retail rentals too (just like a hotel stay), but you will pay more for sure.
If you end up doing a hotel rather than one of those (for shorter stays - like your five night stay, I often for the ease of booking and breakfast included (very convenient if my stay is going to be pretty short without a big grocery store run and I don't have a big extended family group where I really want a balcony and larger common areas), a favorite of mine that I am staying at again for two nights before a cruise out of Port Canaveral in February is the Marriott Residence Inn SeaWorld. I am getting a two bedroom / two bath that has a small common area, table chairs, and kitchen. It includes a pretty nice breakfast. They have shuttles, but I almost always do uber or a rental car for convenience. They have a bar that also does casual dinner options, which is great if you don't want to go out for dinner after a busy park day. The pool area and nice large hot tub are very nice with palm trees and a resort feel. They also (not that you would really need this, but nice perk) provide fast passes for SeaWorld coasters and attractions other than animal exhibits (one per person in your party per day). You just ask for these at the concierge the evening before or morning of any days you are doing SeaWorld (great park!). The Marriott Residence Inn SeaWorld is an older hotel property that very recently went under a remodel, that I think was well done (rooms are cute). Even, though, on my next mini two night stay I am not even doing SeaWorld and am only doing a Disney day, I am staying here again. I looked at tons of different suite hotels and short stay condo options and thought this is my best bet for what I was looking for (anal vacation planner). This one has two queens in one bedroom and a king, so your kids would each get their own bed that is not a pull out if you went with the two bedroom option. I love having the kitchen for teens and twenty somethings who in our family like heating up left overs, snacks, etc. in the evening.