I'm looking to buy aftermarket wheels but I don't want to lower my car. What wheel size and tire size do I need in order for there to be minimal gap without having to lower my car? Thanks in advance.

 

Increasing the wheel without using proper "plus-sizing" will fill your wheel well but will look like your "flying high" cause you'll be increasing the wheel diameter and jacking up your speedometer and gearing.

Also your distance from the ground will increase as your wheel well fills up. This is what happens with 18's, your wheel well fills up but you stand off the ground a little more so you have to lower it to get the effect of a nice low stance with no gaps.