My son was 3 when we first went to Natural Bridge Caverns. He liked it for the first 20 minutes, then got tired. We were down in the caves for probably an hour and I carried him for half of that I believe.
Rudy's BBQ is the place most people go. But I have heard Smokey Mo's is great. I prefer Coopers in New Braunfels. Two Brothers is a little place on West Avenue, and they have a large playground area. The BBQ is good there, but nothing that I consider "excellent." (But my dad says Two Brothers is one of his favorites).
Kiddie Park - I suggest you buy a wristband. I think on certain days it's just $10 and they can ride all the rides as many times as you want. If you don't buy a wristband, you buy tickets and each ride cost one ticket (like at a carnival). If you've never been, keep in mind that this is an OLD park. It's not fancy by any means. Old metal. Defnitely for kids 5 and under. Not above. You can bring a picnic though and sit in the shade and eat. "Central Market" HEB and Witte Museum and Zoo are all nearby there as well. My son went when he was two and LOVED it.
The zoo - we went a few weeks ago. Hot yes. But luckily there are spots that are airconditioned - the reptile house, the frog spot, the hippo area. So you can take a break and soak up some AC when you need to. Small soft coolers are allowed. When I went last I brought water bottles, sandwiches, chips, and drinks for myself and my son.
The only other place we go (in the heat of the summer) is Emerald Rainbow. Google "Emerald Rainbow Spring Branch" and you'll find it. It's an indoor bouncy-house area. Under two is free. 2-3yrs costs $5. Your 5yr old would cost $10. Adults are free. Wear socks. The kids can bounce on different bouncy castles - one with a ball pit, two with slides, one for 3 and under only. You can bowl with mini bowling balls ($2). The putt putt is outside and pretty lame. There is a form you must sign waiving liability. You can find the form online to read over before you go.