texases hit the nail on the head before I could get to it. I have been impressed that Hyundai uses good quality tires on relatively inexpensive cars. Many more expensive cars come with real junk OEM tires. The Elantra in "Limited" trim uses 17" wheels. In order to fit the total wheel/tire package within the wheel well, they install 45 series profile tires. While these wheels and tires "look cool" and might offer a slight handling advantage on a perfectly surfaced racetrack, they are not appropriate for poorly maintained roads. Since state and county budgets are strained more and more every year, road maintenance suffers.
You could get higher rated 17" tires for your alloy wheels at tirerack, but you will have the very same problem with potholes regardless of brand. I recommend buying the cheaper 16" steel wheels that came standard on the Elantra GLS. You can get such "new car take-offs" cheaply on ebay. I bought a set of 4 new alloy wheels for my suzuki for less than $70 (+ shipping) that way. The 16" Elantra GLS wheels take P205/55R16 tires - which will provide far more margin of error when hitting potholes, especially when mounted on steel wheels. The Elantra and other cars that size definitely do not NEED 17" wheels. I had a '65 full-size ford pickup that came with 14" wheels and I never said "gee, I wish this truck had bigger wheels". I saw a Scion today with 20" wheels - which is idiotic.
In addition to using higher profile tires, you must check tire pressure very regularly. I check mine every weekend (along with all the fluids for every car in the fleet). Hitting a pothole with a tire slightly underinflated is the best way to ruin a tire and damage the wheel.
I remember one pothole on the cross-bronx expressway a few years ago that had a long line of cars pulled over with flat tires. As I drove past, I saw that they had one thing in common - low profile tires mounted on wheels larger than necessary for the size car.