There is a track guide on this site. I think it lists all public tracks in many states. On my screen the link is just to the right of the classifieds.
It wasn't that long ago I was in your boat. I looked for all the tracks that said they had a beginner or pewee track so I didn't have to deal with worrying about the big bikes buzzing by him. I eventually bought an xr 80 so I could ride with him and be a shield so to speak for the first 6 months or so of him playing on the big tracks until I knew he was competent and could ride safely with the other bikes.
I remember the first track I took my oldest to like it was yesterday. (7 years ago now) We went to Area 330 because they said they have a pewee track that only a few riders a day will be on it. They also had 3 other tracks that stepped up in size and skill level so as the riders dissipated we could try them all. If you can believe it, he rode two tanks of fuel through a Honda 50 over the course of 8 hours and fought me tooth and nail when I told him we had to leave.
Anyway, you have that same opportunity at Beans Bike Park. (10 minuets or so from Tappen Lake) My suggestion for you would be to take him about half way through the day (around 2 o'clock) start him on the pewee track (behind the house). By 4 o'clock most everybody will be gone and you will have the entire big track to yourself. By then the track will be beat up in the turns but will be smooth and acceptable for the little wheels. You won't want to have him on that track early in the day. He will just get frustrated with the deep soft dirt.
I would put my youngest on the big track late in the day and on several occasions the owner (BJ) would come out after the advertised closing time and let me know we could stay as long as we like. My kid would ride until dark. Beans was the first place he every had a gate drop. BJ still had a working gate and we were the only people there. I set that gate for him a least 50 times that night.
There are several other tracks not far from you that also have beginner tracks, check the track guide.