The aviary is absolutely accessible by foot, just a little hard to find. You have to walk around the ray lagoon, and you can't see the sign and entrance until you round the lagoon because the lifeguard stand and some trees block the view from the opposite side.
A great photo op when your family is done enjoying the birds is to send them back out into the river. Stand on the bridge in the main aviary and wait for your family to come through the waterfall. If they have noodles or colorful vests they can float on their backs and you can get a really neat photo.
There are many areas of the river you cannot walk up to, but you can look out on a few bridges and from when you first enter the park. The caves are only accessible in the water. But you can easily stand on the shore of the ray lagoon, and two sides of the resort pool, the coral reef has limited land access, but there is a back corner on the opposite side of the ray lagoon that would have the "shipwreck" pieces in the background for photos.
