The Waffle House is an excellent place. Breakfast is a pretty easy meal to get without meat. Plus, it's open 24/7. The Waffle House has the best hashbrowns I've ever had and their waffles and toast are good, too. If you don't mind the whole diner atmosphere with smokers and such, the Waffle House is a great option.
Chili's has a special called the soup and salad special. It's a big bowl of soup, plus salad of your choice for $5.99. They have a soup called baked potato soup and if you aren't vegan, it's a really good choice. It has a lot of cheese in it. Be sure to order without bacon, though. Their Caesar salads are the best, too. I also believe they have a black bean burger, but I've never asked about it.
Denny's, surprisingly, also has a couple of vegetarian options. On the breakfast menu, they have a vegetarian omelet, and on the lunch menu they have a veggie burger. Keep in mind they also have excellent hashbrowns.
When going fast food, if you aren't vegan, check out places with grilled cheese sandwiches. Generally they are meat-free. Places like Sonic and Dairy Queen usually have grilled cheeses.