Midstate trail, RI to NH, near worcester:
http://www.midstatetrail.org/map_page.html It has a couple shelters:
https://sites.google.com/site/treksa...id-state-trail
Tully Trail:
http://www.thetrustees.org/places-to...ww.google.com/ Around Royalston, MA, 1 hour NW of Worcester.
Metacomet-Monadnock Trail (M&M Trail), ends at Mt. Monadnock, starts in CT.
Monadnock Sunapee Greenway,
http://www.msgtc.org/map Goes from Mt. Monadnock to Mt. Sunapee (NH) and has shelters a day apart; it's supposed to be pretty nice, but takes longer than an overnight (I suppose you could do an out and back).
Wapack Trail, Mt. Watatic to N. Pack Monadnock; not much camping though (maybe at Windblown XC ski area with permission and fee).
I'd say the Tully Trail would be best for a nearby overnight, staying at the shelter. Closer might be hiking around Mt. Wachusett (lots of trails on Mt. Wach) and the Midstate Trail and spending the night at the Muddy Pond shelter, Westminster, MA.
Bring DEET and headnet.