If you do an away rotation, I would definitely go somewhere with a "good" residency program. It doesn't have to be MGH, Duke, UNC, etc. Just pick a nice program that you think you would like to check out as a possibility for residency. It doesn't have to be your future #1 program; although, if you are going to shine like a rockstar, it may not hurt if it's your top pick. Just remember that top picks may change after the interview trail, so don't put too much emphasis on it. Just make a decision and move forward. Also, you may shine more and get more personal interaction with a PD and/or chairmen at a somewhat more regular program than say MGH. This fact may well play into you getting a better letter out of the rotation. You get the idea.
I would suggest doing a rotation at your home program first to learn the baiscs, so that you are more than ready for your away rotation.
When you are at your away rotation, you can make it a point to meet the chairman and PD. You could get a letter from whomever you jive with the most. I got one letter from my anesthesia chairman (I'm at a medical school that has an anesthesia program which is facing difficult times right now). It didn't matter that my school's program is having trouble, and I didn't even do an away rotation. I can't tell you how many times on the interview trail this year that interviewers would ask, "How is Dr. so-and-so doing these days." Dr. So-and-so may be the chairman of a program with problems, but chairmen seem to know each other. A strong letter from a chairman goes a long way. It just so happens that my chairman was a previous faculty member at one of my top choices, which I did not know until the interviewer at that program mentioned it. Also, my chairmen goes to all the various meetings, so he has friends everywhere just like most other chairmen...that's why they are chairmen.
If you do an away rotation, don't forget to get a strong letter from your own program's chairman. Just be sure to let your chairman know at the outset of your rotation that you are interested in anesthesia. Make an effort to get to know him/her. Try to work directly with your chairmen when the opportunity arises. Don't be pushy, but do make an effort. It will most likely pay off with a nice letter.