Not much in the way of indoor tracks. UVM has an 11 to the mile track but access can be challenging. Racket's Edge fitness center in Essex Junction has an 8 to the mile, but it only has 2 lanes. St Michael's College also has an 8 to the mile but the corners are kind of squarish so it's more of a fitness track than a running track.
For outdoor tracks, Colchester HS is the best. It's well sheltered from the wind, new surface, top quality. Plus they have miles of trails right next door. Great place to do speedwork. The UVM outdoor track is horrible, beat up, exposed to the wind, just awful. The Essex HS track was just resurfaced and I have heard good things, plus that's closer to Williston than Colchester.
For running clubs check out gmaa.net. They seem to be getting more serious, attend most of the NE Grand Prix races and the bigger NE XC races.
If you are around next summer you will want to check out the weekly XC races at Catamount (www.catamountoutdoor.com). They use 2 different 5k courses, both very challenging. Turnout was great last summer, 150+ many weeks.
For places to train, lots of dirt roads north and west of Burlington. St Albans (25 miles north) has a 30+ mile gravel bike path. In the Williston area give Indian Brook Reservior a shot. It's in Essex Center. Great place to run, although only about a 2 mile dirt loop. Still, I could do half my miles there and not get bored.
Any other questions feel free to drop a line.
In addition to Bruce Hyde, David Shenk from Essex Junction HS is at Cornell. David was one of the top HS runners in the state last year.