I dropped by front entrance of the zoo last night and there are no bike racks per se, but there are literally about 30-40 street sign poles with handicapped parking signs right at the front. I believe there is enough space to lock your bike on the sides of the poles nearest to the vehicles so that you won't be blocking the pathway for wheelchairs. On the sidewalk there are an additional 15-20 handicapped parking signs. Many of these are sufficiently far away from the sidewalk so you could lock to them and not worry about impeding traffic on the sidewalk.
Both the Museum of Natural Sciences and the Zoo really need to install some real bike racks. That area is probably one of the most cyclist-friendly places in Houston and I'm really surprised that there is little to no bike parking available.