Grubbs is an absolute STAPLE of Brighton, especially for ending your night out with a deliciously greasy burger (it's open until 1:30am on the weekend). Burgers usually run you about £2-3, chip portions are generous, and they sell good shakes too. There's also a branch closer to Hove, near Palmeira Square.
Grubbs is probably one of few iconic Brighton institutions not to surrender to hipster aesthetics (not that that's always a bad thing). This is no frills at its best; a small waiting area with some barstools and tables, your standard checkered diner floor, chalkboard menu, and walls plastered with flyers.
If you really love their burgers, Grubbs also sells some pretty neat t shirts.