Is there a site or service which works like the yellow pages for OSM data?

There are some commercial sites which have essentially done that. They automatically create one page for every street or point of interest based on OSM data, and display related links and ads as their apparent business model. They seem to primarily rely on showing up in search results for roads and POIs, and are in fact highly ranked for lesser-known street names where there's not much actual content available on the web.

Examples include strassen-in-deutschland.de and wie.de, both of which focus on a German audience and appear to be products by the same company. (Curiously, they use Google Maps for the actual map of the street/POI – even though the rest of the content on their pages is sourced from and attributed to OSM.)

Another example is roaddir.com, which exists in several variants such as roaddir.com/US/ for the US and roaddir.com/UK/ for the UK. In addition to a search box, it lets you navigate down a hierarchical tree from states to streets.

Unfortunately, I'm not aware of an open source implementation of the idea.

We do such a thing in Ethiopia with http://AddisMap.com and try to make it OpenSource. The plans are outlined here: https://openplaceguide.org/ and here: https://github.com/openplaceguide/openplaceguide

If you know the precise tag you're after, you can use overpass turbo (zoom the map to your area and click on "Wizard").

I'm sure there's a better solution, though. :)