I live in Arlington and often ride to work in Cambridge and am constantly riding out to Concord and beyond from my house. As someone who rides in both directions, I suggest that unless you want to brave the Boston streets, I would suggest this. Bypass Boston and Cambridge and hop on the T. Take the redline to Alewife and either:
1. get on the minuteman bike path which goes right by the T stop and follow that out to Bedford then 225 to 62 to Concord like Robyn suggested. But I agree, the bikepath gets frustratingly busy on the weekends.
2. Another option would be to taking the T to alewife then taking Mass Ave. through Arlington and Lexington. Then my favorite part, in Lexington Center the road splits, stay on Mass Ave., go up then down a really fun hill. Make a right on 2A, follow this up and down the rolling hills through Minuteman National Park then make a right on Lexington Road staying on 2A and it takes you right into Concord Center past Orchard House and Nathaniel Hawthorne's House.
Seriously though, riding in Boston and Cambridge sucks, it's dangerous to drive here, and even worse to ride these roads on a bike. To make matters worse, the streets don't make any sense and it's extremely difficult to give directions and very easy to get lost.
Another option if you are staying in Backbay is to ride along the Esplanade. There's a bike path that runs on both the Boston and Cambridge sides of the Charles River and it's a really beautiful ride and it's totally flat. I would go for this ride instead, you get amazing views of Boston and ride right past Harvard's and MIT's campuses.
Good luck!
It's only worth it if you're having fun