Your speedo is calibrated to the diameter of the stock wheel/tire package. Any variation to that diameter will cause your speedo to be off to some degree. Here's a calculator you can use to show you the effects of changing your diameter. Plug in your stock size on the left and the size you're considering on the right to see the effects.
Wheel / tire size calculator / comparer - RIMS-N-TIRES
From a visual standpoint, increasing your diameter may help to fill the gap, but as jshillin pointed out, it will also cause your car to sit higher off the ground.
Plus sizing to a larger wheel with a lower profile tire, if done correctly, will not change the overall diameter wheel/tire package and as such, will not help with the gap. Plus sizing without lowering the car can actually result in a visual effect that emphasizes the gap and causes the car to look raised even though it's not.
The right way to eliminate the gap is to lower the car with lowering springs. That's an expensive upgrade, and will have a negative impact on the way your car rides. You generally get better handling, i.e. cornering, etc., but a rougher ride.