One of the best things you can do for your residency/fellowship application would be research, particularly in the area of a fellowship you're interested in. You can do it in one month, and still enjoy yourself because it's usually not hard. It also doesn't have to be in the city of your medical school. Most faculty are failry approachable and will let you join something if you just express interest. Hell you may even get paid. If you try this, do your best to get your name on a paper as at least a co-author. There is a separate section on the ERAS application just for publications and most applicants put nothing.
