There's no (or at least very little) resistance to adding POIs to OSM. In well mapped areas, the data in OSM can be a lot more accurate than the geocoded addresses that Google often shows you.

There's not really any great search interfaces for it (where part of great is limiting the results to 'nearby'). Komoot/Photon is a nice way to find something you know the name of:

http://photon.komoot.de/

And there are people working on displaying the data that is available:

http://osm24.eu/index.php#!15/52.5173/13.4032/type=eat/mon=p...