Worcester is a shithole. You will only be disappointed.
As for time of year to do a hike? Probably late spring or early summer. Also early fall. Shirley is in a decent area. However, Fitchburg is kind of an armpit, and it's close by. Devens was, at one point, home to 20th SFG. It's still home to the Army Reserves.
Wachusett Mountain State Park has some nice trails, and is not far from Shirley.
Boston, and the surrounding area, has some awesome history. I know it's city stuff, but it's neat to see where this country started.