You almost have Worcester right, it's more like Wuhsta, though. Leicester is pronounced Lester, so you were pretty close. No one has Quincy right yet though, and that's the most telling, you hear it mispronounced all the time on newscasts that don't originate from the area.
Years and years ago there was a plane crash in Billerica that killed some of the top executives from Digital Equipment. ABC News and Peter Jennings was broadcasting at the time, and it was funny to hear him call it Bill-ericka instead of Billricka, which is how it sounds phonetically.