The New Regent. An amazing small venue, had some great nights there.Gawd, how could I forget the Richmond and Sister Rays - The Richmond wasn’t my favourite venue though for some reason (was it the sound) but it was a good size venue. Maybe before your time but there was a small music venue at the bottom of West Street too that was popular with some of the local music promoters - I cant remember the name of it - on google earth, it looks like its been gutted and the name changed to ‘Lazer Zone’ - saw some great bands there in the 80s.
We could add the Alhambra of course to your list - again a great underground venue (literally) for up and coming punk bands of the late 70s.
https://www.setlist.fm/venue/the-new-regent-brighton-england-3d3713b.html