Our section of the New River is very family-friendly. There is about a mile stretch where the river is calm and shallow with a 200 yard section of rapids at the end. Our bus stop at Big Falls Park is before the rapids, so you DO NOT have to go through the rapids to go tubing. 
We do require anyone under the age of 16 to wear life jackets any time they are in the river. You may bring one of your own (make sure it is Coast Guard approved. There will be a label on the inside.) or rent one from us for only $1. Children under 16 must stay on the right side of the river where the water is generally less than 3 feet deep . At higher water levels we may recommend not allowing children under a certain age (depends on the level and their age) to go through the rapids. We do recommend that all children get out before the rapids on their first trip down, so that they may become familiar with the rapids before they go through them. You can get out before the yellow buoys at Big Falls Park and walk down the road, look at the rapids, watch a few other people go through, discuss it with the kids and then you decide who goes and who doesn't. If you do decide to go through the rapids, wade out at the boat ramp far enough so you can float between the yellow buoys. That will set you up for the safest and most fun ride through the rapids.
Tubing with children:
(540) 639-66332591 Big Falls Rd, Blacksburg, VA 24060