Caribbean

Cafe Conscious (182 Avonvale Road, BS2 3LT) - added 18/10/15
'Wayne grew up in Jamaica watching his family cook traditional Jamaican dishes so we decided to start a cafe focused on Jamaican food that was tasty, healthy and ethical.' They have lots of vegan options: Ital Stew; Ackee & Tofu; Vege Chunks; Tofu & mixed veg; Tofu, callaloo & peppers; Veggie pattie. Each of these comes in small or large options - sounds great!
http://www.cafeconsciousbristol.co.uk

Easy Rawlins Diner (28 Chelsea Rd, BS5 6AF) - added 18/10/15
This place has some fantastic-looking cakes. Have a look at this positive review from the Bristol Post and download their menu here. They also hold pop-up restaurants, like this Nigerian pop-up.
https://www.facebook.com/EasyRawlinsDiner

Fi Real (57 West Street, Old Market, BS2 0BZ)
Opened in May 2014, Fi Real is a family-run restaurant that seeks to bring us veggie/vegan food with 'an authentic Caribbean flavour.' They have home-made juice and vegan cake (look at this victoria sponge with guava drizzle and strawberries!), and a changing menu, which currently features escovitched tofu. I love the tastes of Caribbean food, but usually us vegans are out of luck in this department, so discovering this has made my tummy very happy. Will definitely try this place out when I'm (vaguely) in the area.
http://www.fireal.co.uk/visit-us/

Plantation (221-223 Cheltenham Rd [this later becomes Gloucester Rd])
This place is pretty famous among vegans in Bristol, and I gather that it is a regular meeting place for vegan groups. Looking at their menu, it will be pretty obvious why; not only do they have an incredible range of Caribbean food, but everything is labelled (can't you tell that I love labelling?). I don't know about you, but I love the flavours of Caribbean food, and am always really disappointed when I can't eat it because it's meaty, but fear not: from ackee to jerk tofu, Plantation's got you covered.
http://plantationrestaurant.biz