GTN 750 doesn't show towns or cities.
 

Am I doing something wrong, or are they not in the Europe database?

I don't show much geography on the GTN, but you can choose. On the map page tap menu select map set up select land and the choice of city detail should then be obvious. There's an iPad app you can use for training.

Garmin's Label Sizing and Visibility Range for city names etc. is absolute crap for flight planning. I make my plan on SkyDemon then plug the waypoints into the Garmin. It's much easier and as I said elsewhere, Garmin must have had a crack smoking chimp design the flight planing user interface graphics.

It is predominantly an IFR bit of kit so doesn't need to show that much detail, hence no airfields that do not have an ICAO code.

You can of course add your own waypoints/towns etc.

Wot he said ^^^^^^^^. Its a brilliant bit of IFR kit. If you want VFR, buy an Icom radio, an iPad and a SkyDemon subscription.