Trucks are popular largely because they can do pretty much anything. A truck can haul cargo or a trailer with its bed and rear-wheel-drive, or it can use that rear-drive axle to vaporize tires in brutal powerslides. A truck can bomb down a trail like a psychotic warthog, or it can rumble down the boulevard in style and comfort. The Silverado's big wheel openings certainly pay dividends when it comes to fitting off-road tires -- but they can serve just as well as receptacles for hugely impressive wheels.
The stock truck uses 245/75R16 tires, which have an overall diameter of about 30.5 inches. That outside diameter is the safe limit without modifying the truck in any way. In the real world, a 25-series sidewall is about the realistic limit for a truck this size if you don't want to destroy your rims on the first pothole you hit. Given that -- and the same width -- you can get away with a 26-inch rims and 245/25R16 tires. If you keep the same width, and you're not planning on going off-road, you could get away with as much as a 35-inch tire without lifting modifying the truck. That gives you a full 30 inches of rim, with 245/25R30 tires wrapped around them like smears of black paint. Consider this the very outer limit, though, and only for show trucks -- not for daily drivers.
In the real world, those 245/25R30 tires will likely rub while turning or when you hit bumps, and the wheels' sheer mass -- combined with that of the truck -- is going to absolutely pummel the rims on anything you hit. If you're willing to sacrifice a bit of handling and braking, want a smoother ride and want your rims to live a bit longer, you could use thinner 200 mm tires in place of the original 245 mm tires. That gives you a 30- to 35-series sidewalls on 30-inch rims -- tire size 200/30R30 to 200/35R30. This narrower-tire approach is probably the ideal if you want maximum-diameter rims that won't self-destruct on speed bumps or rattle your teeth out.
