The smallest of the three vegetarian restaurants is located on the Pertamina roundabout (Jl. A. Yani and Jl. Jend. Sudirman). There's nothing particularly bad about this place, but the choices are a little limited. They do sometimes have Singkawang noodles, which you won't find at the other places.
Near the main police station on the road to Sukadana (Jl. B. Katamso, on the west side of the street about 50-100m north of the traffic light) is a restaurant that tends to be more popular with foreigners, thanks to the friendly service from the husband and wife who run the place. It's best to go at lunch as they can run out of dishes later in the evening, but they will cook more upon request. The dishes rotate frequently, but lots of soy-based artificial meats, including fish, rendang, hekeng (local shrimp sausage) and my personal favorite sate. A few perks to this place - you can drink a fresh coconut, there's a decent selection of vegetarian ready-made dishes and seasonings you can buy to cook at home, and there's the town table tennis 'stadium' in the back of the restaurant if you want to work off some of the calories.
The newest vegetarian place is run out of the local Buddhist temple, on Jalan Imam Bonjol (on the way to the main market on the edge of town). This used to be an ad-hoc place run on Saturday nights only, but recently has grown into a restaurant open every day. It's a bit out of town but you get a nice view of the Pawan River (and hopefully a breeze). I would go for the self-serve buffet as the nasi goreng/mie goreng options have been pretty disappointing.
At the non-vegetarian restaurants, beyond the basics of kangkung/cap cay/kailan, try the bun tahu or sapo tahu which are cooked with an egg tofu (make sure to be clear about no seafood or chicken!)