Brazos Bend State Park, about an hour south of Houston is the best place to see the American Alligator right now.
If you can make it to the park during the weekdays, it isn't crowded at all and after the gate opens at 8am, is the best time to see them on the move.
40-Acre Lake, the Spillway Trail and Elm Lake all have many gators and lots of waterfowl. Lots and lots; more than you will see all day in the average wildlife refuge.
The backside of Elm Lake can be accessed by car, if walking is not possible for you, so get your binoculars, some sandwiches for a picnic and come on down.