Probably the nicest hotel walking distance to everything would be the Renaissance (nice four star hotel). This is a beautiful property and gets terriffic reviews on Trip Advisor too. On a smaller budget, the Hilton Garden Inn next door is a great little property (three star hotel -- I've stayed here many times). The nice little pool and hot tub, great kid meals for room service that are only about $5, etc. have made this a great choice on little three night stays to do SeaWorld with DS.
If you want a little more room, the Hilton Grand Vacation Club SeaWorld is a great walking distance choice -- not sure, though, being a condo, that it's on the preferred property list. Depending on how long we are staying, a condo is something I really like on a family trip.
I haven't stayed at the Marriott Residence Inn, but DS has when he attends SeaWorld camp and I've seen good reviews. It's a too far to be walking distance, but quite close. They have shuttles, a great breakfast, and a little more space if that is appealing. // Kind of like a cross between a condo and a hotel.
Have a wonderful time. Sounds like a super vacation.