This place is legendary and does offer a decent pizza for vegans. Pepe's base "tomato pie" is cheese-free by default, though they do sprinkle parmesan unless you tell them not to.
I stick with the base tomato pie and make it vegan without the parmesan. Adding toppings gets kind of pricey, but a medium pizza is large enough to feed three people prettily easily.
People rave about the crust at Pepe's and, while it's good (kind of chewy, kind of crispy), I guess my Chicago origins leave me preferring something a bit heftier.
What makes Pepe's great, for me, is the sauce: it's simple and just full of flavor. Beautiful bright red roma tomatoes, garlic, olive oil.....just wonderful.
My only gripes with Pepe's is the consistent waiting time. If you get there early (before 6 p.m.) or late (after 8:30 p.m.) you probably won't have to wait, or at least not wait that long.
One suggestion for improvement would be to add some specialty vegan options, such as Daiya cheese, as well as some mockmeat toppings. They're easy to source and would attract a much larger audience. That said, a simple, no-frills Pepe pie is still a great meal.