Is there a particular city or region you want to visit?
The state is very beautiful throughout. You do not have to go far to find its charm. My recommendation would be to setup base camp in a state park (tent or cabin), hostel, or B&B, and take daily trips from there. Excellent choices include Middlebury, Rochester, Woodstock, & Waterbury.
For a full loop, try one that combines all the cities I mentioned above + Burlington. The ACA Green Mountains Loop can give you a few ideas. The loop itself is 376 miles, longer than what you are looking for. You can use it to think about a loop around Lake Champlain or CT river.
Take a look at the Lake Champlain Bikeways map for ideas to ride in the valley with spectacular views of Lake Champlain, Green Mountains, & Adirondacks without the big climbs.
For a one way trip, try to see the entire state along route 100 from Canada to Massachusetts. There are several touring companies that offer this trip.
I can try to give you more details once you decide.