Parking in Montpelier
Downtown options are described here: https://www.montpelier-vt.org/
If parking near town and carpooling fewer cars in is an option, the park & ride near the interstate is your best bet (included on the map here: https://en.parkopedia.com/
There’s free parking on the streets outside of the immediate downtown, though the closest are often full during the day (like Court St by the State House).
For a 5-minute walk to the State House, there is often room to park on the streets in the “meadow” neighborhood, down Elm street: Spring, Summer, Winter, Pearl & Vine.