The peak season is Easter. I would go any other time without making reservations. Two campgrounds are good for biking. Rio Grande Village with flush toilets and Cottonwood campground with pit toilets. Both have water points. I would do two nights at Cottonwood (biking to Santa Elena Canyon) and most of my time at Rio Grande Village (biking to Boquillas Canyon). (They're at opposite ends of the park, kinda.) You might take the Class C down the road a ways to the Hot Springs and bike most of the way (the road's too tight for a C). Be sure and hike back to the spring. The Chisos Basin is good for hiking and warmer at night since its at a higher elevation than the other two campgrounds. The only in-park restaurant is there. That campground has flush toilets. Check the mileage from the campgrounds to the canyons, your daughter may not be up for that long of a bicycle ride, but some of the way would be interesting anyway. Look for the finger-sized barrel cactus in the rocks on the uphill side of the tunnel (they have little pink flowers in the spring but you'll miss that). Just get out and walk some, you'll be surprised at what you can find. Ranger walks and talks are great! Attend all you can.