The city certainly wants to be bike-friendly (see this initiative by Mayor Marty Walsh on making Boston into a "world-class bicycling city"), but it still has a ways to go. Some comments I have are:
1) Bikes tend to get stolen a lot. I don't know how the rate compares to other major cities for comparison, but you can see on this map that there were hundreds reported stolen in the greater Boston area last year alone. I know this is fairly normal, but it's still a bummer and worth making note of.
2) Since the greater Boston area includes many bodies of water, some areas are just not accessible by bike alone. For example, East Boston is separated by tunnels and bridges suited only for cars and trains. To get to/from East Boston with a bike, you'd have to either strap your bike onto a car and drive, put your car on a bus bike rack, or bring your bike on to the T (Boston's subway/metro/tube...which does not allow bikes on trains during what it deems peak hours). Also, if you're commuting from one greater Boston neighborhood/city to another, that route is often not safe for bikes. For example, biking from Somerville to Medford and back requires you to cross an almost unprotected crosswalk that cuts through a highway on ramp.
3) Bikes are extremely dangerous to ride in the cold (below freezing), as roads are slick and often bike lanes aren't plowed. Boston's below freezing temperatures can sometimes stretch from the end of November to the beginning of May.
4) Boston drivers are notorious for being angry and aggressive. Expect to be yelled at a lot, and to not be yielded to.
That said, if you're living in and commuting to neighborhoods within in the center of Boston (Back Bay, Southie, Allston/Brighton) or within a specific, close area outside of Boston (like just the Newton area, or just the Cambridge/Somerville area) biking can be a lovely experience during spring, summer, and fall.
Another thing to consider is using Hubway, a public bike share system instead of your own bike, though it tends to shut down many stations during winter.