Is it Dorster, or Dor-chest-er or something else. It is sort of like Worcestershire. I grew up calling it "Wooster" sauce... (I know). Sometimes I call it "What's this here" sauce but I think it is wors-ter-shire... but I'm not sure. You probably need a cockney accent to correctly pronounce it... but I digress, Dorster?
What is next? East something? I think East Farthing would ROCK!
 
J

Locally it may be pronounced " Dough-chess-ta"

I think it's "Dork hipster" or something like that.  

In a broad Dorset accent?
 
('course, that would be the UK Dorchester.)

Glyn Barnes
In a broad Dorset accent?
 
('course, that would be the UK Dorchester.)

Dahhrrrrchesturrrrr

It depends on whether you're in Massachusetts or Great Britain, two places that have many placenames in common, but often with radically different pronunciations.  Oddly, it's the normally enunciation-lazy Americans who retain all the letters and the normally more-precise Brits who run them all together and/or drop them entirely.
 
I used to live in a town named Bicester, near Oxford. It was pronounced "bister". I didn't even attempt to say any town names out loud when I visited Wales.

It's like Worcestershire but with a D.
 

Tourists in New York always get confused by the fact that Houston St is pronounced "Howston" and not "Hewston" as in Texas. I've had tourists tell me on more than one occasion that I'm saying it wrong, even though I've lived a block a way from the bloody thing for 10 years. 
 
I'm going to say with 99% certainty that Dorchester is pronounced exactly how it looks. 

 
There are no doubt exceptions*, but the general rule over here in Blighty is that place names ending in:

• ---chester are pronounced phonetically, e.g:
  • Man-chester
  • Win-chester
  • Col-chester
• ---cester are pronounces so the "--ce" part of the suffix is silent, e.g:
  • Worcester = Wuss-ter (as in Wusstershire Sauce)
  • Leicester = Less-ter
  • Gloucester - Gloss-ter

* Cirencester is the only one I can think of, and is pronounced phonetically, albeit with a soft 'C' = Siren-sess-ter
 
 
 
 
===================================
(PS - how long [i.e. 'short'] is the time limit for silent editing in the CH?)
 

Daw-chest-uh