You have a couple options. By far the most popular is the
Holiday Inn Sunspree resort, which is literally
across the street from Vista Way. There are also other hotels (
Courtyard, etc) within a very close proximity of the area. Search for "Lake Buena Vista" on the popular travel search sites for hotels in the area.
I would recommend staying in LBV as opposed to an airport hotel. That allows you to start your check-in process really early on, and if you time it right, leave your bags in your hotel room until you're fully checked in, when you can head back to your hotel, check out, and then move your bags into your apartment.
A shuttle fare via
Mears to the general area is about $19.