It always sounded to me like the slight accent was on the first syllable, with the last two falling off: PEE-buh-dee.
I live in Worcester, Ma and it is most commonly pronounced “Whister”, not “Woostah” by people who live here.
The north shore folks (where Peabody is located), specifically Lynn folks (next town over, where my family is from) would have pronounced it PEE-BIDY. It’s a clear marker for folks from that area.
If you were really local, and/or lived there, it would just be Riccah. I once listened to a book on tape that had characters in and out of the “House of Corrections” there, and it was anguishing to listen to as they pronounced it as Bill-ERR-ica. It was horrible to listen to, especially as I’ve worked in the town, and went to school with lots of folks from Billerica who taught me in no uncertain terms how they pronounce it. The author was local, or had enough experience in the area to properly describe the area, but the reader obviously wasn’t, and it wasn’t reviewed by the author.
The Woburn, Peabody, Billerica, Worcester pronunciations always tell me that a local business has outsourced their voice work on their ads, and didn’t proof the recordings well enough. I’d be far less inclined to frequent those businesses if they can’t care enough to get the correct local pronunciations correct.
There’s not much to love about Bicester.
Actually we pronounce it as Wis-ster. Leominster can go either way.
Dorchester is Door-chester with more of a short “o” sound.
(yes, I’m from MA – why do you ask?)
Ohio is rife with this kind of thing thing. I used to near Mantua, Ohio, which has signs at the town limits proclaiming that it was named for the famous Italian city. But it’s pronounced MAN-uh-way.
We also have Milan (MY-lun), Lima (LYE-muh), Russia (ROOSH-ee), and Versailles, which is of course pronounced ver-SALES.
I’ve lived in Memphis for the past four years, and I’ve only heard it pronounced how it’s spelled (PEA-Body).
Maybe a true Memphian could vouch for me, or correct me.
(I didn’t know until a local informed me that McLean Avenue–a major street in midtown–is pronounced “Mc-LANE”).
Bisster? Well it’s not too far from Worminghall (Werminal)
My wife’s grandma lives in Froncysyllte and even after many visits I still can’t say it “properly”.
We have a village here called “Beausale” which ends up as “Bowsull” (or “Buzzle” if you’re proper rural).
OK, I’ll defer to that. 
‘Siren-cester’ is correct though, because I was there yesterday and checked on it by stopping all pedestrians and asking them how Cirencester is pronounced.
(If my sample was small it’s because most of them ran away.)
Which is actually the correct pronunciation.
I’ve also heard PEE b’dee. Or as my boyfriend likes to bring up, their police department: PEE b’dee P.D.
The other thing about Mass that confuses the crap out of me is Dedham - DEAD’m, Needham - NEED’m, etc…but it’s Raynham - RAIN ham and Wareham - WARE ham.
I’ve also never known how to pronounce Effingham…either way, it’s slightly inappropriate… EFF-ing’m “She was Effingham,” or EFF ing ham, as in, “Ma, pass the Effingham. And the effing gravy while you’re at it.”
My wife grew up in another Broughton, in Hampshire, which is pronounced the same as the Milton Keynes one. The next village along is called Houghton, which provides yet a fourth pronunciation - it’s “Hoe-tn” (although some locals say it should be “How-tn”).