Stay at university for summer or apply for other research programs?
Think about what you want for a career. Don't try to nail it down too firmly yet, but think about the options. Do you want an academic career? If so, you will want a research doctorate at some point (beyond a medical doctorate, perhaps). In that case, having a publication and some research done early will be a boost. Your current situation is more likely to result in a publication than a short term REU, I think. Also, if your relationship with the PI is a good one, it is less risky to stay where you are. 

But if medicine is you real goal then research publications are probably less important and getting a broad outlook will probably serve you well. 

The trade off is specialization vs generalization. Having a broad view of all that is possible in the world is a good thing, but academics at some point need to specialize in quite small areas. Your call, of course.