Vermont is a very cool place. Especially this
I'm also a newbie on this forum - and more importantly, still new to fly fishing, but this crew is generous with advice. OTOH, I've lived in Central VT for 40+ years. I'm pretty sure you can find many spots to keep you busy, and part of the charm is exploring them over time.
You didn't specify the kind of fishing you're looking for, but...
Start with the VT F&W web site: Vermont Fish & Wildlife
As for winter fishing, things have recently changed. See this news release:
Vermont Fish & Wildlife
I'll also send you contact info for a couple of the primary fly shops in the northern section.
I don't get to Lake Champlain often, but for some it's a draw. I'm more interested in the streams and small ponds. As for ponds, check the Dept. of Nat. Rec. site for a chart of fishing in State Parks. Google & Google Maps is your friend.
Here's a partial list of rivers to get you going:
Winooski River - Marshfield to Burlington
Mad River - Warren to Waterbury
Lamoille River - Johnson to Lake Champlain
Otter Creek - Middlebury
Battenkill - Manchester
Conn. River - "east coast"
Paul Stream - Maidstone
Willoughby - Orleans
You might want to concentrate on the streams in the north & northeast sections since many others were blown out by TS Irene 2+ years ago.
PM for clarification.