I've always wanted to try paddling across Long Pond, in the St. Regis Canoe Area, and climb Long Pond Mountain. That might be a good one. There are also numerous campsites on Long Pond. Nearby is also Floodwood Mountain, which you can't paddle to, but might be another good hike with a young child. In general, there's lots to do in the St. Regis Canoe area that involves both paddling and hiking.
You might also try paddling in the Lower/Upper St. Regis Lakes area. There is a nice loop that you can do from Paul Smith's college. Launch into Lower St. Regis Lake, and paddle down the St. Regis River to the St. Regis Mountain trailhead. St. Regis Mountain itself is a 6 mile round trip, which might be a bit much for a child that young. From here, you can carry into Upper St. Regis Lake. There are three lean-tos in the vicinity, one on the St. Regis River, one at Marvin Pond midway through the carry, and one on North Bay a little ways beyond the put in at the end of the carry. All of these sites are on publicly accessible easement land, and any one of these sites would be ideal for camping. There is also a public lean-to on Lower St. Regis Lake at Peter's Rock; during the spring and fall it is frequented by Paul Smith's students, but only a few students are around in summer during summer session. Note that the lean-to on the esker on the northwest side of the lake is private and not open to the public.
From North Bay, you can easily paddle across Upper St. Regis Lake into Spitfire (there is a great spot for swimming at Rabbit Island, although the island itself is private property the water is shallow), and from there back into Lower St. Regis again. For hiking, you can also carry from the St. Regis River into the outlet of Black Pond, at the Paul Smiths Visitors Interpretive Center (VIC). From Black Pond you can carry into Long Pond. There are numerous trails throughout the area, including a trail up Jenkins Mountain, which, if you paddle devote most of a day to, could potentially be suitable for a three year old. Note that, even though there are 2 lean-tos on Black Pond, and 1 on Lond Pond, this area is day use only.
Why not try the Lows Lake area? Hitchins Overlook is an easy climb up to a rocky summit overlooking Hitchins Pond. The trail starts right by the foundations of the Lows estate. You could easily combine a paddle to the upper dam and this hike in a single day, even with a three year old (although I'd probably get an early start).
Lows Lake, though, is best enjoyed via an overnight trip (it sounds like this is what you are looking for), which will allow you to get into the actual lake itself. There are numerous campsites scattered all along it's shores. There is a short trail to Deer Pond, starting from the west end of the lake, although it's at least a full days paddle to get there. If you carry into Deer Pond, you can continue across deer pond and take another carry into the headwaters of the Oswegatchie River, and from there continue downstream. The trail from Deer Pond also continues to Grass Pond, and eventually, to a junction with the Cranberry Lake 50 at Cowhorn Pond. With a three year old, though, unless you are doing the traverse, Deer Pond will probably be enough of a hike. There is also a trail north out of Grass Pond (which you can paddle into from Lows Lake) to Chair Rock Flow, but again, it's probably more than you'd want to do with a three year old.
Hope that helps!
