You can query the REST endpoint of a hosted feature layer in ArcGIS Online. However, there's no option to measure the distance from the input geometry. That would require a geoprocessing task of some kind. A quick search didn't reveal anything like that available in ArcGIS Online but I'm not that familiar with that stuff.
Here's an example hosted feature layer and here's a URL to query the first 8 records within 100 miles of the input geometry (point as lon/lat). Changing the f=pjson to f=html will let you see the all the query parameters available.