What fields/properties can be queried from Facebook Graph API on a Place object?

If you leave out the "fields" attribute in your query you will get all the fields. The number of fields depends on the object type (for example owned pages vs. wiki pages).

Don't just look at the Graph API. Take a look at FQL. There are different fields available in FQL vs. the API.

And yes, using the distance function you can look for places in an area.

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