I suggest that you do a search here on Boston hotels as this question is raised and answered several times/month. You should be aware that Boston is often listed as being in the top 5 cities in the US for cost of hotels. "Clean and close to public transportation" - true budget hotels do not exist in Boston and you are looking at over $200/night - more in peak season. In fact, if you find something that looks like a real bargain, I suggest you post here since it is likely it has some serious flaw - most likely safety or difficulty of commute to the city.

Hi
My favorite Boston hotel is the Marlowe, actually just over the river in Cambridge. Can be pricey, but watch for deals. It's part of the Kimpton group so it includes wine hour and lots of fun amenities like free bike and kayak rental and a super staff.
About two blocks from the T (the green line) and just around the corner from the Museum of Science.

Otherwise you can get reasonable deals out near the airport and take the T into the city each day. Even if it's a bit more expensive than other cities, it's definitely worth the price!

We enjoy the www.newburyguesthouse.com

The Midtown (www.midtownhotel.com near Prudential Center and Northeastern University; on the T's (subway) Green Line-E) usually has rates under $200, as does the Buckminster (www.hotelbuckminster.com Kenmore Square a block away from Fenway Park; Green Line-B) if the Red Sox are out of town.

To go over $200 but not stratospheric, try the Holiday Inn Beacon Hill (www.hisboston.com Red Line Charles/MGH) or, close to the waterfront, the Harbor Inn (http://harborsideinnboston.com/ few blocks from Red, Orange, and Blue Lines).

Another good place for suggestions is www.boston-discovery-guide.com/inexpensive-boston-hotels.html

Many stays in Boston to go to Mass. Gen. Hospital (relative with long illness)
always stay at John Jefferies House..steps put door to 'MTA' 1-2 blocks to restaurants,cafe-even a little grocery (this is Beacon Hill area) Out the door and over footbridge and can walk along the Charles River. Rooms are "quaint" in a good way...Great bathrooms and each room frig,stove, microwave and utensils..adequate breakfast in lobby.
Studio room is small but very comfortable.
Check web site..
note all lodging in Boston-14.5 % tax--really makes the bill go up quickly !!!
http://johnjefferieshouse.com

We liked the Courtyard Marriott in Brookline:
http://www.marriott.com/hotels/travel/bosbl-courtyard-boston-brookline/

Wow, the Newbury Guesthouse must be popular. I just looked for dates at the end of June and it is full already.

When are you coming to Boston? Rates vary quite a bit depending on what events are happening around town. And what's your budget? www.lastminutetravel.com often has "mystery" hotels but it's fairly easy to decipher what hotel it is. Just come back and ask if you find one.

Also check travelzoo for deals. The Boston Common Hotel often has more modest rates and is located near Copley Square, not the Boston Common.