Finding a self-funded research internship for summer (international student) - any strategies?
Not very organized, but here goes.

Make a list of your specific interests (not just for now, going forward: are you interested in graduate school or work afterwards?). Areas of particular interest? Make a list of potential schools, their strengths (and possible non-matches with your interests, "weaknesses" is just too strong a word). Look which ones most closely match you. Check at their policies with respect to students like you (do they have an office for foreign students, or some equivalent?). Try to contact students/student ombudsman/... for a insider view. Check for alternatives for housing (it can be rather expensive, specially if you need to pay for utilities!). Check the courses offered, see which ones are near your interests. Check what requisites the courses ask for, see if you have them (or can learn them on your own).

In the end, this is a very personal decision, it is very little we can offer apart from general drivel like mine.