Nothing specific from me; just the kind of info to use when you get stuck...
When Bloomerg still had their groove, they had a joint along Nkrumah Road.
Other joints were located on Moi Avenue, from 'Pembe za Ndovu' all the way to Kilindini posta. (Especially opposite the tourist office, near that turn-off to Ganjoni)
If all fails, the good old Canon Towers should have a few more joints to explore.
PS : It's been a while since I was in Mombasa, I expect that such shops have mushroomed everywhere.