Solid ol' Saiva Kade in Jtown.
Hotel Rolex and its misleading name are an experience not to be missed whilst in Jaffna. Hot, juicy biriyanis and sugary juices. This is legit Northern saivar kade territory.
Amaage is probably the largest restaurant in the area. They do decent kottu.
Fits' Margosa in Chunnakam, Jaffna is an elegant refurbished 19th Century mansion about 9km away from the main town, and possibly one of the only upscale hotels at the very North.
The original Rio Ice Cream parlour is old and sweet- it's persisted through decades of war and strife as an integral part of the local community. It's worth a diabetic shock or two to experience that.
One of the better eateries in Jaffna, with a wide variety of Northern Sri Lankan food
Casuarina Beach is the go-to beach for Jaffna locals. Don't expect a bikinis-and-beers sort of scene.