Visit Big Bend
Golf (you can probably find a more conveniently located and better golf course)
Sneak unmolested back and forth across the border (for the sheer hell of it)
What to do at night when in Lajitas? The choices are limited. You can get sloshed on over-priced drinks at one of the very few watering holes in Lajitas. You could go for a walk and get a better look at the stars (the celestial variety) than you have probably seen in a long time or you can f*ck.
If you chose f*cking, remember to bring your own. In Lajitas, this is as tight as they come (see photo).
Dress Code: for drinking ... just bring your wallet
for walking & looking at the night sky - bring your boots
canoodling - up to you