Bowling Alleys?

The general tag is leisure=bowling_alley. You should also tag it with sport=10-pin for US style 10 pin bowls, or sport=9-pin for various different European styles (English skittles, Kegelsport). You can browse places mapped with this tag here. (It may be that many bowling alleys are tagged with leisure=sports_centre, but the more specific tag is to be preferred).

At least in Europe facilities range from large standalone places with 10s of lanes, through small places with perhaps only 8-12 lanes, and then down to single bowling alleys located in pubs. One of the larger ones in Zurich is located in the basement of an Italian restaurant.

I dont think that other forms of bowls (petanque, crown-green bowls etc) in indoor centres are tagged with this tag.

It does not look as if anyone is tagging details of number of lanes etc, but this could be done, something like bowling_alley:lanes=## would be a reasonably clear way of doing this.

Don't forget that many bowling alleys may offer other facilities, such as a bar or restaurant. These can be mapped too.