Warping or kedging is a method of moving a sailing vessel, typically against the wind or out from a dead calm, by hauling on a line attached to a kedge anchor, a sea anchor or a fixed object, such as a bollard. In small boats, the anchor may be thrown in the intended direction of progress and hauled in after it settles, thus pulling the boat in that direction, while larger ships can use a boat to carry the anchor ahead, drop it and then haul.
Things like the Rion-Antirion bridge pylons, submarine tunnel segments etc always reach their final position with warping.
A floating sea city would be no different. Warping it into an ocean current, float to the other side of the ocean with the current, drop anchor in the target area and warp again to the final position. A some 30 miles a month can be achieved with very small winches.