When you look at tire sizes, the first number is how wide it is in MM. (so a 215 tire is ~ 8.5" wide, a 225 wide tire is 8.85" wide and a 235 is ~9.25" wide.) the next number is a % of sidewall to tread, and it factors in the wheel size. so a 225/65r16 is 8.85" wide and and 27.5" tall, a 225/65r17 is the same 8.85" wide, but it is 28.5" tall, so a full 1" taller despite the other numbers being the same.
You can read more about it at tire rack:
http://www.tirerack.com/tires/tiretech/tiretech.jsp
and you can plug a bunch of different tire/wheel size options into a tire conversion calculator that will give you more details on overall dimensions:
http://tire-size-conversion.com/tire-size-calculator/
I PERSONALLY would not go up to a 18" wheel for a few reasons. 1) it will not help you get a bigger tire anyways, you max out at a 28.5" tire overall diameter without modifications and up to 9" wide depending on wheel. 2) Tires are harder to find in that size that will fit the patriot. 3) tires are A LOT more expensive the lower profile you go. 4) it totally ruins the ride. When you get a shorter sidewall that means your suspension has to work a lot harder at keeping the ride smooth, where your taller sidewall tire used to take up a lot more of that work. A low profile tire has a very stiff sidewall on it.
If you want to ditch the 16" wheels, maybe got to a 15" wheel, A LOT more tire options (especially a "light truck" tire which I think fits the patriot a lot better and will last longer) Cheaper tires, improve ride quality, and, of course my personal preference, it looks better.
if you go after market and get something with less back spacing (so like a 4" back space) you could possibly fit a slightly wider tire on there without modification. Tires, even if they are the same size, are not all actually the same size (kinda like shopping for pants. I wear a 38/32, but only sometimes, Sometimes I'm a 36/30 and sometimes I'm a 40/32, all depending on the cut of the clothes and the overall design.
Guys have fit 235/75r15's with just a hammer to flatten the stupid pinch weld in the back of the wheel well, and even 30x9.5r15's without too much rubbing (not saying none, just minimal) and if you squeeze one of those puppies in, then you have your 2" of lift over stock without any real modification.
of course that is all personal preference, and if you dig through the suspension and tires section, you might find a setup that you really like:
http://www.jeeppatriot.com/forum/forumdisplay.php?f=16