We went through this with our daughter. There are a few 20" bikes, but they are hard to find. We found more mountain bikes, then anything. We finally went with a mountain bike, which has held up pretty good. I think the most important thing is to get a bike with good gears and brakes.
We were going to change out her tires from mountain to road tires, but now she wants to try mountain biking. The problem is that mountain bikes are pretty heavy because of the shocks.
We found our daughter's Specialized Hot Rock at REI and I believe they had another 20" bike in Sports Chalet. Those bikes are all over Craig's, used and for sale.
Just take a look at the gear and brake cables. You know cheap when you see it.
Also, I thought bikes were a one for all. It is pretty important that he sit on the bike and feel comfortable with it.