UNC Chapel Hill has had a program in the past...they have some research didactics along with the research assistant position. Most everyone gets some type of publication or presentation out of it. When I did it, several years ago they had mostly their own students but also some from other places. Dr. Jane Brice was in charge.
In Ohio Summa Health System and Akron General Medical Centers have programs for the med students from their own schools for summer research and sometimes there were outside people working with those programs as well.
Contact the dept. office directly for any places you're interested in going...the worst they could tell you is no.