Ice fishing in the backcountry

A friend and I were looking to go for a snowshoe into a backcountry pond/lake on our way into Lake placid in February to ski whiteface. We're driving in early from the Niagara area through Buffalo. The plan would be to hit a trailhead in time for a late lunch... Preferably at a lean to. I'm guessing we'd like to keep the distance down as time is a bit of a factor.

We'd consider doing some ice fishing too. The problem is most hike-to scenic ponds are trout ponds.

Can anyone suggest any ponds or lakes that meet this criteria...

- along the way to LP from Buffalo (there are many different routes we can take)
- 1-2 miles(ish)
- scenic
- lean to prefered
- legal to fish (perch / walleye / pike)

Thanks!