The driving portion is an important part of the game, and is carried out one of two ways: by hitching a ride with a passerby (borrowing it GTA-style) or by purchasing a famous Simpsons car with gathered coins, like the hulking snowplow Mr. Plow or the soapbox racer The Honor Roller. Each car has the typical attributes of acceleration, handling, etc., which makes some cars more desirable for certain missions.
A fast sports car would be advantageous for the racing mission against Principal Skinner, while a heftier vehicle that can take a lot of damage would be better when looking to smash Mr. Smither's prissy luxury liner. All cars, though, handle exceptionally well even when using the WASD keyboard layout. Of course, this being primarily a console game, picking up a gamepad would be your best bet for optimal control.
On the streets, Hit and Run brings the town of Springfield to life. Sidewalks bustle with activity, and you'll notice many a recognizable Simpsons regular. Huge billboards line the highways, advertising popular events from the series like the Truckosaurus show or the Springfield Dog Race track. All the Simpson stores, from the Moe's Tavern to Lard Lad's Donuts, can be entered and interacted with. You can also pick up money throughout the town, which can then be used to purchase the aforementioned vehicles, or even upgrade your wardrobe. With this much stimuli to take in, training yourself not to ogle the surroundings becomes the biggest hurdle when it comes to learning the basics of Hit and Run gameplay.
Heading out on foot reveals another layer of intricate game detail. You can walk into houses and restaurants and interact with the Simpsons characters you've come to know and love. Head over to the Quik-E-Mart and you can talk to Apu, who is sitting behind the counter listening to Indian sitar. Apu's freezer contains that old fogy Jasper, who put himself in cryostatis, and is patiently waiting for a future thaw. These encounters play out just like the episodes, and there are many little touches and inside jokes that you will want to play it twice to catch them all.
Naturally, you refer to a game as "Grand Theft Auto inspired" without gratuitous violence, and Hit and Run does have a degree of it, only with a Simpson's twist. Fox might not take to well to a game that can have Homer perched up on the top of the First Church of Springfield with a Sniper Rifle taking out Millhouse from 300 yards so they lightened it up with more "cartoon violence". Running people over with a vehicle will either knock them down or send them flying in the air (often inciting a curse or two) then they roll around on the ground for a while and get back up with no hard feelings.
When on foot, however, you get no weapons of any kind. No flamethrowers, knifes or submachine guns. The only weapon you have is to kick people. The effect is the same as running them over: they roll a while then get back up. But violence isn't without its consequences and if you boot enough people to the ground you get paid a visit by Springfield's finest officers, who will doggedly pursue you Keystone Cops-style in their police car. If caught, you receive a hefty fine in coins. The "violence" in the game appears to be an afterthought, added in to make it more like GTA, but it keeps the game's focus on completing the missions and soaking up the environment, which is plenty to keep you occupied.