They have a nice golf course - Tierra Santa. Just east of Weslaco in Mercedes they've opened an Outlet Mall. I haven't been there, but I've heard it has a lot of good stores. South Padre Island is about a 50 minute drive. If you go South of Weslaco to Progreso, Mexico you'll find some good authentic Mexican restaurants. During the Winter, the place will be loaded with Winter Texans. The restaurant I usually go to is Arturos.
I live in McAllen, so I'm not as familiar with Weslaco and I'm totally out of the night life scene, but I've loved growing up in the Valley.