Cheshire Medical Center/Dartmouth Hitchcock Keene (N.H.). Located in Southwestern New Hampshire, between Boston and Hartford, Conn., Cheshire Medical Center is a 169-bed regional referral center joined with medical practice Dartmouth-Hitchcock Keene, which boasts more than 125 providers. In 2014, CMC/DHK was accredited by The Joint Commission. In 2015, iVantage Health Analytics named Cheshire Medical Center HealthStrong Top Hospital.