Sorry, Kellie - There isn't anything like a campground or overnight parking at Old Sturbridge Village that I know of, but there might be large rig parking in the lot for day use. I never noticed in the past and haven't been there in awhile. Perhaps there's a WEBsite for them with a phone number or e-mail contact. There are a few RV parks nearby and I'm sure there are probably tour shuttles.
You sound as vehement about having electricity as my Dad used to be about NOT camping where there was electricity. He always wanted to "camp" not "RV" (as he would keep reminding me). Whenever we followed each other traveling around this great country, he would always look for the no amenities campgrounds (often free). I would put up with that for 2 or 3 days and then insist on a RV park one night! So you see, there are probably enough people who want the more primitive campout experience to fill the campgrounds. If you don't think so, just try to get into one of the state parks over a holiday weekend! My solution for you if you can't dry camp is to stay in private RV parks and sign up for tours of nearby attractions.
I have travelled all over the country in my 40+ years of camping, in every state of the lower 48. I found many, many public campgrounds without electricity and many, many with - everywhere. I have found some pretty fantastic private parks and some pretty bad ones. It's part of the deal when you become a "camper" or "RVer".
Most importantly ---- ENJOY THE JOURNEY!!