magi there's one called the Market Place on Meeting House Lane which runs from Prince Albert St to North St with a bit of a wiggle. Last time I was there the selection wasn't great.
The other one is at the bottom of Elm Grove, just off Lewes Rd, it's called The Vapour Trail, part of a growing franchise I believe. Bit of a grim area, I would advise driving there and doing a bit of cowboy parking on the pavement - like everyone else does! You could go there on your way in, or out. Lovely, helpful people though.
May I gently correct you on something? The North Laine (no "s") means the North Field in old English and refers to the whole area below the station between Trafalgar St and North St, down to the London Rd.
You know where The Lanes are. It's confusing as pronunciation is the same, but a bit of a niggle for old Brighton pedants 
Have a lovely day, hope sun shines for you.