I think so! You can bike or take the bus to most places around campus/Chapel Hill and Carrboro, and then just use Zipcar if you want to go further, for example into Durham.
As for vegetarian restaurants...well, not all of these are vegetarian, but as a veg*n I tend to find they have a wide selection of veg*n options:
-The Spotted Dog (in Carrboro, actually is 100% vegetarian)
-Carrburritos (excellent burritos)
-Cosmic Cantina (Franklin St., burritos and quesadillas, but not as good as the one in Durham)
-Mediterranean Deli (Franklin, also supplies packaged lunches to the various campus dining halls and convenience stores if you want to pick one up; there's a convenience store near-ish Sitterson)
-Artichoke and Basil (Franklin, pizza)
-Pepper's (Franklin, pizza)
-Buns (just off Franklin, best garden burger on the planet, hands down - I suggest getting it with wasabi mayo, avocado, and a side of sweet potato fries)
-Kurama (next to Buns, conveyer-belt style sushi with vegetarian options and inari, not the best quality but cheap/fast/oddly thrilling)
-Akai Hana or Shiki Sushi (in Carrboro and Durham, respectively, if you want decent sushi with vegetarian options; the latter's regular Japanese food is also excellent)
-Bandido's (Franklin, though again the one in Durham is better. I recommend the spinach quesadilla or the spinach burrito with salsa verde but I'm a spinach freak)
Hope this helps!