What is the northernmost/southernmost city that receives no snow?
On the North American west coast, Coos Bay, Oregon is the northernmost place I can find, of any significance, that gets no snow.  Astoria, Oregon gets 2.5 cm of snow per year.  Coos Bay is at 43.4 degrees north latitude.

On the east coast, Boston is of similar latitude and gets significant snow, so that coast is out.

In western Europe, A Coruna seems to be the best candidate, at 43.4 degrees north in Spain.  I had originally thought Guernsey would be a good candidate but it gets a little too much snow, and cities in France seem to get regular snow too, even on the coast.  Venice looks like a tempting alternative, but it seems to get snow consistently, if uncommonly.

So, so far, 43.4 N seems to be the answer on both the North American and European continents.

In the southern hemisphere, Comodoro Ravadavia, Argentina at 45.8 S gets snow, but Trelew, Argentina at 43.3 S does not, so the snow band in eastern South America seems to be quite close to the same latitude as we see in western North America.  There are few significant communities on the western Chilean coast, but Puerto Montt, Chile is snow-free at 41.4 S.  Southern New Zealand is at similar latitudes, but seems prone to heavy snowfalls at times, probably because of its proximity to Antarctic currents and the presence of tall mountains.

There are quite a few southern islands that are candidates, but most seem to get snow, and none have any significant settlements, short of the Falklands, which definitely do get snow.

If you get rid of the people requirement, the McMurdo Dry Valleys at 77.3 S are probably the answer.  They are very cold, but so arid that they are largely snow-free all year long.  Snow that does try to fall often sublimates directly into the atmosphere.