Don't have any experience with the parks in Lake George. We typically avoid that area in favor of the other parts of the Adirondacks. If you have 3 weeks to work with, my recomendation would be to hit a couple stops between LG and the Falls. Old Forge (Old Forge Camping Resort, or one of the many great state parks) would be worth a stop.
Then make a stop in the Finger Lakes when headed to Niagara Falls. Watkins Glen has a KOA or a good state park (reserve early for electric) and/or stop at Letchworth SP.
In Niagara Falls, we stayed at the Niagara Falls ON KOA last year. Very nice, great location, and priced accordingly - plus you have the border crossing. But if you are going over, check them out. We also stayed at the Grand Island KOA on the US side in June. That wasn't a bad cg and the location is convienient. There are some good state parks up on the shore of Ontario, but they are farther away from the Falls.
Have fun! Should be a great trip.