All branches of the White River are unbelievable trout streams. Not off the beaten path at all, these are world famous. The first branch, especially from the Tweed River on downstream, will have you ready to move to Vermont permanently. That's what I did, back in the 1970's. I fished all weekend, got a post office box on Monday, and called work to tell them where to mail my last paycheck. Cross the bridge in Gaysville and turn left, upstream. At the fork in the road, bear left, go a few hundred feet to a pulloff on the left and walk a short way to one of the most productive pools on the river. At the tail of the pool, you can catch rainbows all day long. Above the pool is some swift, deep water with large scattered boulders on the bottom. Almost impossible to fish from shore, this run can be effectively fished by drifting from inner tubes. Hang on !! Between the boulders are HUGE brown trout.
The best statistic about Vermont is that there are native brook trout in every piece of running water in the state. Use the Bethel VT area as home-base, pick a few feeder streams that run into the White River (from topo maps) and go exploring. Most of these fish are small, but there are the occaisional larger ones - I caught and released a 14" brookie in Camp Brook. The little ones are delicious. A very short 5-weight rod works well in the smaller streams. A 7 1/2 foot 7-weight for the White and Connecticut Rivers.
In late April and early May you can have a blast fishing landlocked salmon from the cut in the causeway heading out to the islands (S Hero) on Lake Champlain. When the water temp approaches 53 degrees, the place really lights up. Start just before first light. A nine-three, grey ghost or other smelt imitation, not more than 2" long and sparsely tied is just the ticket there. Have some straight-up and some weighted on hand.
If you are in the Burlington area early in the year, look into the warm water discharge from the wood-chip electric plant (North end of the plant). With decent polaroid glasses you will see (from shore) an amazing raft of lake trout finning in the current. I think they line up there to rid themselves of lamprey. They don't really seem to feed. They will accidentally inhale a small weighted fly if you are patient enough. Even if they don't, the sight of all these fish will get your heart pounding.