I do a couple things to look for cities in OSM…
If I’m in the OpenStreetMap site, and I am looking for a single place, I’ll zoom waaaaay in to where I expect it to be & right click & choose “Query features”. This will update the left column & I’ll look through the “Enclosing features” list for a good match (sometimes one doesn’t exist).
If I’m looking for cities in general within an area, I’ll use Overpass and run this query while zoomed into the area (swapping out 8 with other numbers, if it doesn’t produce results - usually 9 or 6):
[timeout:900][out:json];
(relation['admin_level'='8']({{bbox}}););
out geom;
