Visiting from CA, one day to see some TX birds/wildlife, where to go?

Hi! I'll be mentoring a Californian high school robotics team who will compete in Houston starting April 20. I extended my own stay a little bit after the kids go home, gonna check out NASA JSC, and I'm also a hobbyist wildlife photographer. It'll be nice to spend a day trying to photograph some animals that I can't find in California (I collect these photos, label them, and make my own sticker book, it's like stamp collecting but animal photos).

I will not have a rental car, just Ubering everywhere.

Where should I go?

On your current front page, there's an alligator by a river and the comments indicate that people have named it and feed it food. Is that typical? Should I go there? (I'd be pretty happy to add an alligator to my collection)

Where else? Somewhere that Uber can reach from the hotel (near the Houston zoo, no zoo/farm photos allowed in my collection), and doesn't require going off trail. (I won't be familiar with your park's etiquette about staying on trail, so I'd rather just be cautious and respectful)

I don't need the rarest of all sightings, I don't want to stand in one spot waiting for something. Like… in my area, we only have one breed of chickadees, the chestnut-backed chickadee. So even a black-capped chickadee would make me extremely happy (which is also not in TX, it's more northern, but it's an example).