Hi Kizzy
I did an OS uni visit, but it wasn't for as long as that, it was only for a couple of weeks. My uni had a partnership with a US uni, and so I knew who I was going to be working with. Beforehand I organised a study tour for myself - I emailed all the experts in my area, sent them background info about my research and then went and interviewed them all. They all provided really useful feedback. I think if I was going for a 3 mth visit, I'd have a discreet research project in mind, one that could only be done by visiting that country. I'd use it as a small research project which would fit into the larger research in my thesis. In my case, I'm using some theories developed by American academics, and so I used my visit to talk to academics about these. I also interviewed some industry people too.
Could you think of something along these lines maybe? Go to a campus which specialises in your area, work with academics on a small research project to support your larger one?
My 2 weeks were invaluable, not only for the knowledge I gained, but also for the self confidence it gave me, knowing that I could get around by myself in another country, something I'd never done before and which I was really nervous about. Go for it!