Hi Kacee -
Glad to see you are interested in Peds!
I think if you do a search you'll find some answers to your questions but I'll put in my 2 cents on a couple NE schools. In brief, I think there are some programs who will interview you if you did a rotation (the one that comes to mind is CHOP) while there are other places that may not interview everyone (I would do a search - I think Boston Children's is quoted as one program that does this).
I would use your externship / elective time to figure out more if the place is a right fit for you. Remember that it isn't all about the name etc... Rather, you want to find a place where you feel like your goals are well matched with the goals of the residency program. I was pleasantly surprised on the interview trail to find a ton of fantastic programs across the country which had great training programs in place. Rarely did I find a place where I said to myself, "This is not going to be a good training environment."
In anycase, I digressed. If they interview you and you rotated there, it is a great opportunity to talk about your experience and the Program Director/Chair of the Selection Committee will chat with your residents & faculty to get a sense of how you performed. I think people have mentioned that the away rotations are a double-edged sword. If you perform well, you should be performing just as well @ your home institution (you need to show consistency). If you don't perform well, this can hurt your application.
As for places to do a rotation, honestly, you can't go wrong. You have lots of choices in the NE. My 2 cents is for you to figure out where you might be happy (aka do some research at the different programs) and then apply there for an away elective. Do something you are passionate about and you'll shine as well as have a good time. For me, I did an away elective in Peds Oncology and had a blast. I used that time to get to know a program that I had done some research at from a clinical standpoint. Yes, I worked hard and while I don't think it impacted whether or not I was going to get an interview, I believe it was very helpful post-interview to help provide another perspective on my performance.
Hope that helps!
Cheers.