Back home we used to ride our bikes quite frequently, mainly because we like to do exercise outdoors, and we decided to continue in that path once we moved to Boston.
One of the very first things we did when we arrived was to buy two nice bikes that would allow us not only to continue exercising but also to move from place to another. I find that Boston is a very friendly city for bikers. Most of the avenues and many of the streets have bike lanes, especially in Cambridge, where students use their bikes a lot to move around campus. It is also very common to see moms and dads taking their little kids for a ride in the bike trailers.
One of my favorite rides is along Charles River. The bike lane seems to never end. I like to start on one side of the river and then cross to the other side in any of the many bridges that cross the river, and go back the other way. I like to feel the company of other bikers and runners and the river view is very relaxing.
Another very nice ride is The Minute Man Trail (http://www.minutemanbikeway.org) which I did a couple of times with my friend Laura. To get there, we took the red line (yes, you can take your bike in the T off peak hours) and got off in Alewife station. From there it is a five minute ride to the trail, which runs from Arlington to Bedford. One of the nicest things of this trail is that since it is surrounded by woods you ride in the shade most of the way, which is very convenient in summer. I recommend to go during the week if possible because it can be pretty crowded in the weekends.
Regarding rules and regulations, I recommend the following website: http://massbike.org/resourcesnew/bike-law/
As you will see, it is not mandatory for adults to wear a helmet. However, I strongly recommend that you do so if you are planning to bike.
Typically it is quite easy to find where to park your bike, for which you will need to have a good lock. I do not recommend the regular ones (chain + lock) because they can be very easily opened or broken. U-Locks (by Kryptonite for example) are a good option.
One last recommendation: Ride safe! Enjoy your ride!