5x112 to 5x112 will fit, but the tire combination is notably wider and taller. You can compare them at any tire-size calculator/comparison website, but roughly: the 215/60's will be almost half a inch wider and about 1.3" taller. Someone will likely tell you "they will fit" without knowing about your car, but actual fitment depends on the car/suspension: Some instances (where you would fully expect a new combination to fit) don't work out because a car is lowered or has worn out suspension. Generally, however, a VW on 16 inch wheels will be able to handle most other 16 inch combinations, as long as they aren't too dramatic (stock 15, 16, and 17's were common, and 18's common with the Mk7).
Also note, if you aren't familiar with swapping new wheel/tire combos, the steel wheel will also (generally) be heavier, as will larger tires. Combine a heavier wheel with a heavier, wider tire and you'll likely see a quick loss in FE, especially in the city. The new combination is also taller, which means fewer revolutions per mile. This means your speedo will read differently (the calculators will provide specifics), and the mileage on your odometer will be under-reported. These can be adjusted via VCDS if you have it, but many people don't care about the speedo, since most German cars are set to over-report speed by a few mph.
Lastly, I see you're a snow guy from Madison. As you probably know, narrow tires actually do better in many snowy conditions, and many New Englanders buying snow tires will go one size narrower than stock. I run only Nokian snow tires (Hakkapelittas), and generally try to reduce width by 10mm, depending on what's available and pricing. HTH.