Worst case kill is never.
I think kill it asap, don't bother investigating 1 move south, when we destroy the city we would gain the same info, and be 1 turn ahead on scouting. We could do with the gold, and we should have 99.5%+ chance of winning each battle anyway.
We also should scout south east with Barentz IMO.
We know we have trade routes with MS and Kaz, but not with Cav. If that is the barb city that is blocking the trade routes, then we know MS is to the south east, and if we uncover the rest of that river leading towards MS, then we will get trade routes with MS. MS might also be a little more talkative if Barentz is on their border as well.