Can anyone help me find a hotel near the down town center that doesn't cost an arm and a leg? Or, can anyone tell me about a hotel that is near public transportation that takes you downtown? We will be in Boston in October and do not want to rent a car.

Boston in October....an inexpensive room...forget about it.. It's leaf peeping time and "head of the Charles"..... you had better start searching for a bed and breakfast..

Marilyn,
Hotels (at least the nice ones) in the downtown area of Boston are very expensive. However, you can stay out of the downtown area and still not need your car, as long as you're close to one of the T (subway) stops. For example, the furthest location on the Green line (the Riverside stop) is in Newton, and that's only a 20-25 minute ride to downtown. There's also a Holiday Inn right next to the station. The subway (I use the term loosely, as it runs above ground as much as below ground) also has a stop at the airport, and you can transfer between lines at several locations.
So what I'm trying to say is, you don't need to choose a hotel in the center of town. Pick one slightly out of downtown to save money, and you'll still be able to see the city with very little inconvenience.

Marilyn,
How long will you stay there? I stayed in Boston in July and I rented an aparment for 575 a week. It was in Back Bay, close to subway, Prudential, Copley Square...
I think there isn't any hotel more cheap.

Give this number a try -- 1-800-332-3026. It's called 'Boston Hotels'. They're, for lack of a better word, a clearing house for the hotels in the area and may have a good deal for you. Check it out, it can't hurt, it's a free call.

Also, that Holiday Inn in Newton isn't bad either if it comes down to it.

Boston Hotels
You might try the Constitution Inn in Charlestown. It is on the bus line and within walking distance of downtown. It is located in the YMCA. I work by there and see many tour groups staying there. I think the rate is $99/night.

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Try the Boston Park Plaza hotel...while I live in Boston, I was searching for a less expensive room in the middle of it all for some friends - found a rate of $149 per night.

October is tough...spend more on the hotel and DO NOT rent a car.

Don't forget! You get what you pay for....And watch the neighborhood that you are in. Stay in the Back Bay if you can.
The Park Plaza is a great hotel in a great area....it is old, but very up to date and rooms are nice. I have stayed there many times....just stayed at the Fairmount Copley....very old and it shows...if the $$ was coming out of my pocket (instead of my company) I would have been asking for some money back!!
Marriott Copley also very nice.