What to do with a badly-placed city?

Trading it sounds like a bad idea given the placement and you cannot destroy cities you have founded (although an enemy could, getting that to happen is unreliable and dangerous), so the most viable option is to leave it be.

Given that it is surrounded by water and every water tile provides +1 gold, I would attempt to make it a gold-generating city.

Make sure you improve and work any sea-based resources within range (ie, that one fish tile) and build a Lighthouse (for +1 food per water tile) urgently. I would also improve and work both the jungle and gem to maximum production output - the city won't be getting any from elsewhere, so maximise what it can get. Then concentrate on buildings that aid population growth (Granary, Aqueduct, etc) and boost money output (Market, Bank, etc). If the city beings to grow too large then convert some of the population to merchant specialists to pause population growth and generate more gold.

Progress will be slow, but I can forsee the city being useful in the long run.