There are a number of public shore access points, such as from Rogers Rock State Park in the north end. From there, it would be feasible to do a long swim to get to some impressive drop-offs and walls at the base of Rogers Slide.
In other parts of the lake, there are also some old docks that are accessible from shore, I believe. Reportedly, clay pipes and old glass bottles can be found in the mud there. I don't know the specific location or how to gain permission to dive there.
I always used my own boat when diving Lake George. I've done about 30 or more dives there over multiple trips. Good shoals, drop-offs and rock formations can be found on some fishing maps and sonar and/or gps can put you right where you want to be. In fact, a mile or so across from Rogers Rock State Park is a very steep rocky point called Anthony's Nose, where there are underwater walls and boulder piles dropping quickly to 140' or more. The visibility in Lake George is so good that at 140' on one dive, I shut off my light and was still able to see adequately about 10'. Amazing, really!
Finding lost fishing and boating gear was fun, as was having good to excellent visibility (25 to 50' quite often).
Although I never arranged it, I had always wanted to dive on some of the historical wrecks, such as the Land Tortoise radeau, a well-preserved military vessel lying in about 105' of water in the south end of the lake. It can be dived if permission is obtained from the state:
The Land Tortoise Underwater Preserve Site - NYS Dept. of Environmental Conservation
As far as diving solo, Lake George won't present challenges that can't be anticipated, as it usually has temps in the low 40's down deep, minimal current, good vis and moderate boating activity. The last might become a bigger and more unpredictable risk, however, as I'm sure you know from diving Cape Cod Canal.....
Good websites for Lake George diving info:
http://users.wsg.net/sandon/lake.htm
http://www.lakegeorge-vacations.com/lake_george_scuba_diving.htm
Dave C