Hi there
I lived in Florida for a while and now travel to Florida about every 2 years or so. Usually staying as far away from the theme parks as I can.
You are travelling during their busy time so be prepared for lots of snow birds .. US people from colder states migrating south for the winter!
Most of the rental properties are south west of down town and not too far from the parks but are in gated communities so you don't feel like you are in Disney! They should have their own pool or access to a shared one. Davenport, Tuscan Hills, Highland reserve etc are all around the same area found off the I4 highway.
Personally, I'd keep going on the I4 towards Tampa and St Peterburg. You can get to all areas on the gulf coast in about 3 hours max from Orlando Airport (assuming that's MCO and not Sanford which is further north)
Towns such as Sarasota, St Petes Beach, John's Pass are gorgeous, white powdery beaches, lots of restaurants and good night life.
We usually plan a night on the way back to stay in Orlando, do a park or 2 and fly home on the Aerlingus evening flight. That's enough for us.
If you need any help on specific locations, please feel free to PM me.