The grass would be the least of your problems. Seriously though, if you could find a large tractor with an enclosed cab that might be the best way to go. It would be slow, but heavy and durable so you could just ride over the zombies without a big risk of damaging your vehicle. With a little modification ( sheet metal or bars over the windows, maybe a bulldozer blade on the front) you would have a fairly zombie proof mode of transportation as long as you could find fuel to run it.
fuel for something this big would be far too scarce youd need something small because A. Good Gas Mileage B. The Streets highways would be far too cluttered with wreckage and other debris to get through and you cant just risk damaging your form of transportation
I'm going to go with a Short school bus. Its maneuverable, the windows are hard to reach, its designed to have more MPG, and its easy to reinforce, not to mention it has a top hatch and a back door for escaping incase something goes wrong.
Most vehicles will only tip at high speeds, and with something that size, speed wouldn't be very necessary as long as you modified it well enough that zeds couldn't break into it. And, it's still large enough to carry quite a bit of supplies, including any gas you're able to siphon or otherwise acquire.
the best veicle all depends on what u need to do. if u wana get away u need a choper. if u wana make rounds around the city and look for provistions u need something strong and monuverable but still have room to move and a sunn roof is good for mounted machine guns. it all depends on the situation. best to have options