Stay at university for summer or apply for other research programs? I am currently a 3rd year undergrad who assists with research at my current university. I have been working on a project since September 2019, and the PI says it is possible to get a publication with further work (though I know the project is still relatively new now). Should I assist with research in this lab for the summer, or apply to other programs like REUs? 

I received the opportunity to attend a REU last summer but chose an internship instead. For reference, I am hoping to attend a medical school in the future - I hope it's ok for me to post on this academia stack exchange since it is research-related. Thank you for reading!
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.