I have a stock 2013 Mini Cooper hardtop and was wondering how wide a tire I can go with new 16" wheels

 

According to this http://libraryofmotoring.info/facts/wheels/ the stock tire size for 16 inch wheels is 195/55/16. I'd go wider, with 205/50/16.

 

Could I get away with a 215 tire while leaving everything stock?

 

I know some people run 225, so 215 shouldn't be a problem. I have 205 and there seems to be room for a wider tire. Are you talking about aftermarket wheels or stock 16 inch wheels?

 

common sizes:
195/55-16 24.4" tire diameter
205/50-16 24.1"
205/55-16 24.9"

less common:
215/45-16 23.6" (requires 7" or wider wheel)
215/50-16 24.5" (limited choices)
215/55-16 25.3" (limited choices)

more popular options:
215/45-17 24.6"
215/40-17 23.8" (limited choices)

 

+1 stock is 195/55/16 for the 16" Some plus size a bit.