While driving back from our roadtrip to South Padre Island, my husband and I stopped at Laguna Atascosa Wildlife Refuge. This park is special because it is one of the few places you can see ocelots and green jays in the US. Ocelots look like miniature leopards, and about 30-40 (out of the less than 100 total in the US) live in the park. Unfortunately we didn't see one (but seeing one is also complicated by the fact that they are largely nocturnal). However, we did see plenty of green jays! These are really pretty, colorful birds that live mostly in Central and South America but can also be found in Southern Texas. Even if you don't have a strong interest in birds, these are striking enough to capture your attention.
Since it is a wildlife refuge, Laguna Atascosa doesn't have a lot of facilities for visitors. However, they do have some nicely maintained trails, as well as a tram ride around the park. This seems to work in favor for the animals there, because you get a sense of how "wild" the local nature is immediately when you enter the park.