If you decide to go toward the Mission/McAllen area,
Bentsen Palm Village RV Park is a great campground. Adjacent to Bentsen Rio Grande Valley State Park and The World Birding Center. The RV park has lots of activities and facilities. Full hookups including WiFi and cable, Absolutely beautiful landscaping and sites, on site laundry, workout room, woodworking shop, shooting range, craft room, weekly entertainment at the clubhouse, many organized activities, a good guest services staff to help you find what you want to do, ATV and kayak rentals on site, free admission to the State Park, free loaner bikes. and more. Convenient to shopping and services.
They do fill up for the winter season, so it's best to get early reservations if you want to stay for an extended time.
Weather is moderate - highs in the low 70's, lows in the 60's - most of the time. Every once in a while they get extremes of 90's or 40's. In 10 years there, we only experienced freezing temps once, and then only for a couple of days.