You might not like this, but Pop or another value is my best suggestion. Why? Because to stay off property, you'll need a rental car. The cost of a rental car will likely offset much of your savings.
Second, look at Disney's pricing structure. If you are going to do Disney for at least three days, then adding extra days is about the least expensive thing you can do in Orlando.
WE've done many of the "other" things in Orlando over the years. We've always come away saying, "We spent HOW much doing this?!?!? When we could have just stayed at WDW." Though I have yet to go to the pretty botanical gardens in Orlando - they always seemed too far away - on the north side of the city. EVerything else just seems a little lame- Sea World, Universal are about the best, and They're not cheap. Though if you are skipping WDW altogther you could go Universal for an entire week on the cheap.
There are a few inexpensive things to do on-property:swimming, resort exploring, monorail riding, DTD, seeinga movie.
To save money consider AP rates, maybe
DDP. Even eating off property might not save all that much money (unless you research where you are going to eat). Eating breakfast in the room will save money. Bring a box of cereal, a few non-perishable snacks - get some milk and oj.
Last fall we stayed at the Vistana at a great rate. It is off-property, but very close. IT was very clean and HUGE. I was able to get it well within your price range. No great water park, but it was a nice pool. Full kitchen.
(too cold to really swim while we were there though).
We also stayed at AKL for the second half of the trip, and we all agreed that staying on-property is the way to go for our family. It was just so much easier.
I don't know rates, but if you want off property with a cool pool look at the Nick Suites and Caribe Royale. Both have awesome pools.