Brighton Beer Dispensary is a great (but small) pub just off Western Road. It serves a large range of craft beers, which are marked when vegan. Be careful if you try Quadzilla, it's great, but it's about 12%. Lager Not Lager is also lovely, but a more sensible strength!
They also serve food, there is a veganised version of pretty much all of the items on the menu. Between us, we tried the Vegan Pulled 'Shroom Bap (pulled mushrooms, BBQ sauce and slaw) and the Vegan Bangkok Satay (spiced edamame burger, satay sauce, pak choi and red cabbage). The Pulled 'Shroom Bap was very tasty and had a great texture. The Vegan Bangkok Satay tasted good, but was a bit dry in my opinion and that made it hard work towards the end. They also do loaded fries that we've yet to try, but one of my friends highly recommends it.
It's a shame there's not more space in here, finding a table, especially for more than two people can be difficult, but it's a brilliant pub so no wonder it's popular.