For a quick fix that doesn't include tearing down whats already up--I'd think of the empty pool space as the lower level of a multi-level deck...I'd plant more flowers/greenery, paint/stain the deck to make it look less drab, and put some comfy chairs around a great big fire pit in the center...you might have to move the tree and stones for that, but you get the idea :)

I can't see a ton of detail from the picture above. But the first thing I would do is probably add railing and some fragrant, floral vines (check with a local nursery to see what grows well in your area) along the lattice to grow up and over the railing. Once I had the vines started I would work on a path and vignettes. I can sort of see this garden looking a bit like a secret garden with lots of green, flowers, and statues partially hidden by foliage.

depending on the size of the yard itself, set up a projector and a screen for excellent outdoor movie viewing...since the tiered seating is already set up. :)

I second MyAliya's suggestion of thinking of it as a multi-level deck. Maybe you could add a low deck in the center, too.

I'd just put it on Freecycle or on Craigslist as "Free if you remove it", because I'd want the backyard space. That way, the lumber gets used, but you get your yard.

Turn the lower area in to a large curved "conversation pit" by building benches against the inside curve. You could even make them with hinged tops if you need storage for outside cushions or toys.

Or put a fire pit in the middle and logs in a circle around it! S'mores every night! :D

Thanks for the great suggestions! I'm definitely leaning toward the fire pit idea as well as making it into a "secret garden".