-- Last Updated: May-19-12 10:01 AM EST --
I am heading up there again myself in August. From where you're staying, a trip up & back on the Raquette River seems like a must-do; starting at Axton Landing would make a day trip up to the falls achievable, with a side trip into Stony Creek ponds.
If you paddle the length of Tupper Lake, you can visit the Bog River falls on the south end, there's a nice picnic area there.
The Bog River (put in south of Horseshoe) is gorgeous paddling -- the portage at the upper dam may seem a little far with a heavy boat, but it's wheelable and worth it. You could take a break there and hike up Lows Ridge for a tremendous view. Upstream of there maybe a mile or so, there's a floating bog to contend with which you'll need to portage/drag over on the left bank (river right), then paddle from left to right to squeeze around the other piece of the bog. If you paddle as far as the open water of Lows Lake, try the more secluded southern route past the snake-like esker island (the northern route has a scout camp).
In the SRCA you could do the Floodwood/Fish Creek/Rollins loop if you can put up with a couple of short portages; or paddle further down into the Fish Creek Ponds and up into Follensby Clear, then back the same route. Further north at Paul Smiths you could explore the St. Regis and Spitfire Lakes; from Spring and North Bays on the west side, there are hiking routes up St. Regis Mt.
Speaking of hiking, I would very highly recommend Ampersand Mt., which is close to where you're staying. It's quite strenuous but the view from the top is one of the most amazing things I've ever seen.
(edit) I've gotten alot of great info from the Paddling and Trip Report sections on the Adirondack forum, http://adkforum.com