Away rotations ARE a good way to learn about other places. If you have the time and money to live somewhere else and have a good learning experience go for it. They might also be good for applicants that aren't sure they want to do neuro and have weak neuro departments at their home school. I just wouldn't do an away rotation with the primary purpose of trying to improve my chances of matching at program X.
In fact, if I did an away rotation, I might do it at some places I was considering, but not at my very top choices. Maybe use it to figure out where I should apply. Want to get out of the Midwest in winter? Always wanted to live near your buddy in Phoenix? Want to try test out your medical Spanish in Manhattan? Go for it. I would probably go somewhere that is going to give me the benefit of the doubt if I mess everything up the first 2 weeks Im there.
The risk of away rotations is that since you don't know the system somewhere else, where stuff is, etc. you might make a less than favorable impression and hurt your application. And at competitive programs that is going to be a problem, since other applicants are going to have stellar credentials. No matter how hard you try when you are visiting, just in terms of working the computerized medical record, putting in consults, finding the bathroom, etc. you will at times come across like a MS3 from July. Not that many busy residents and staff like showing a med student how to do everything in late fall when everyone else knows whats going on. You need to consider the odds of doing below average or average vs. the chances of really wowing your team.
You pick the letter writers for your ERAS application, but if you do an away rotation at hospital X, the program director there IS going to get your staffs input whether they liked you or not. In fact, at extremely competitive med schools it may be difficult not to be overshadowed by even the MS3s simply by the fact that they know where stuff is, how to write orders, etc. Perhaps you could work one on one with staff on an outpatient service to avoid this.
For some of these reasons, students will occasionally do a rotation at their top choice institutions in departments they are not applying to. Seems strange, I know, but some like that they get to live in a different city and see how people act at a hospital without the pressure of trying to impress everyone. I have known ENT applicants to do a G-surg rotation elsewhere, medicine students doing ER, etc.
Overall not that big of a deal. If you want to try neuro somewhere else, go for it. Just know it is a minor part of the neuro application process and has the potential to both help and hurt your chances.
If any IMGs have different advice for international applicants please speak up.