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Lake George area... climbing at Rogers Rock... I bring my girl up there with some kayaks and it's usually a freakin blast. Rogers Rock campground is also great but I don't know about cabins.. they have showers/flushing bathrooms.

If you just want to boat and don't care about being too close to a lot of climbing, then Lake George is the best bet. There's Roger's Rock if you like runout slab, and plenty of smaller crags all around there. Not sure of other places to boat. Saranac Lake? You'd be almost as far from the classic stuff in Chapel Pond pass.

Lake placid proper is your best bet, but lakeside is not cheap. Lots of stuff to climb and hike within 30 minutes of Lake Placid, Mirror lake right in town. Plenty of things to do and see and eat and wander about when you aren't on the rock, in the woods or on the water.

If you can get around the private bathroom part and can live with dorm style showers and have flexibility the ADK Loj Mid week specials are great. A private room with queen bed and all meals for 3 days for two is going for $575 right now. That puts you on Heart Lake (kayaks and canoes on site), hiking in the high peaks, back country cragging, and Lake placid is a short drive, as are Pitchoff, Chapel Pond, etc.

You could also try Homeaway and see if anyone has some good deals for private cabins or apartments.