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Jaffna's cuisine embraced the peninsula's limitations and evolved in glorious isolation from the Indian subcontinent and the rest of Sri Lanka. Accordingly, Jaffna food is very different from the rest of Sri Lanka's and, when you visit, you might want to try some.
Good luck with that! Jaffna is still getting used to being open after 4pm so places to eat out are still few and far between.
The only place we found, after two or three hours walking around Jaffna town asking for crabs and kool, was Green Grass Hotel and Restaurant, +94 221 222 4385, off Hospital Rd. It was a place a friend from Jaffna (who now works in Colombo) found for us. It is different from the usual dark, dingy places that dot Jaffna town in that the tables are set in a big garden with a gaudy fountain.