My Paleo/Primal family and I live in Northwest Austin and think this is a great idea! It might be nice to meet at a park or hiking trail and do a potluck. Some of my favorites:
Walnut Creek Park - This has picnic areas and even a BBQ or two (probably not big enough :p). This is my absolute favorite place to go trail running and it also has a huge community pool. A lot of dog owners tend to hang out there, so everyone could bring their dogs as another poster suggested.
Town Lake - A good first spot to meet, since it's pretty hard to miss the statue of Stevie Ray Vaughn. More trails, water, nearby cafes and picnic spots, etc. Parking is terrible though.
360 Bridge Overlook - This is one of those park by the side of the road type deals, so no picnic tables or anything here, but there are amazing views of the water and there is a flat spot that would be nice to spread blankets. There is a trail here too, but it can get somewhat mosquito-y.
The best way to get this off the ground is probably to make a Facebook group or another website where things can be coordinated.