The Seaport Hotel just south of downtown, across the street from the World Trade Center Boston, absolutely rocks! Phenomenally well-appointed hotel, very comfy & luxurious. There's a nice B&B on Mass. Ave. in north Cambridge, about halfway between Porter Square and Alewife, but I can't for the life of me remember its name.
Boston is not like San Fran, where you can find a bike route leading you to a nice scenic place from the hotel or where you can easily assemble your bike in the airport and take it onto the subway into town.
It is a hassle to get your bike from the airport to downtown Boston. Leave it in the case so that you can take the Silver Line.
There is only ONE bike route in the entire state. It takes you from Boston to the Cape and I would not advise you to follow that route. There is a bike path that you can take from Cambridge, but I would not recommend travelling to Boston solely for the sake of riding on the path.
If you want some quality cycling near a nice hotel, then I would suggest checking out a B&B or hotel in Cohasset or Scituate. The weather is still holding out for the moment and lots of people cycle in the area.
The CRW(crw.org) has a ride through Scituate at 7AM on Sundays. The cue sheet for the ride is on the web site. I also did a veloroutes.org mapping of it. Just search for CRW rockland.
If you want to ride with a mellow group of guys we have an informal group ride in Hanson(jct of Rt 14 & rt 58 - 30 miles south of boston) at 9 AM on Sundays. You get to see a few farms, cranberry bogs, and some animals. It is mostly for the coffee.
I would highly recommend the Scituate or Cohasset options for a trip in the next week or two. Otherwise the cold and ice will ruin it for ya. The train line is not in service, YET. I would recommend renting a car from Boston and driving to the area.