Montpelier sits on Interstate 89, about 40 miles southeast of Burlington and 145 miles north-west of Boston. The drive from Boston is three to three-and-a-half hours via I-93 and I-89; from New York City it is closer to six hours.
Amtrak's Vermonter runs once a day each way between Washington DC and St. Albans, stopping at the Montpelier-Berlin station three miles west of downtown (a $20 taxi or a local bus). The journey from New York Penn Station is around nine hours — slow, but it cuts out the drive. Burlington International Airport (BTV) is the nearest commercial airport, 40 minutes by road; a few daily Greyhound buses also serve the city.