There's tons of small lakes and streams in the ADK's, and plenty of remote ponds. The Siamese Ponds Wilderness has a lot of small lakes and ponds that you need to hike to get too. The other side of the road is West Canada Lake Wilderness which hold even more. I would suggest figuring out where it is you'd like to go and take things from there.
A few tips:
Don't count on a lean-to. Pick up a couple of small packing tents to sleep in or a three person tent. Sharing a lean-to with strangers sort of sucks. Make sure the tent will allow you to stow your gear.
You're going to need a bear canister, it's actually a regulation if you are in the Eastern High Peaks area from April-November. At minimum, if not in this area a bear bag for food. Read up on how to sue and set one up. They don't just keep your food from bears, but raccoons and other scavengers.
Ice out and snow melt brings a lot of flooding up there, and at times trails can be impassible and or dangerous (even the flat ones). Keep that in mind. Flash flooding up there's no joke.
Remember, May starts the black fly season and it runs until August. Sharing camp with those little bastads sucks more then sharing a lean-to.