I was going to suggest you could wrap things up in a table-valued function so you could query something like this:

SELECT * FROM [dbo].[ufn_example_by_area_amenity]('Auckland', 'cinema')

Function would look something like this:

CREATE FUNCTION [dbo].[ufn_example_by_area_amenity]
(
  @area NVARCHAR(MAX),
  @amenity NVARCHAR(MAX)
)
RETURNS TABLE AS RETURN
(
  SELECT
   [type],
   [id],
   [lat],
   [lon],
   [amenity],
   [name]
  FROM OPENJSON
   (
    [dbo].[clr_http_request]
      (
       'GET',
       'http://overpass-api.de/api/interpreter?',
       CONCAT('data=[out:json];area[name=%22', @area, '%22]-%3E.a;(node(area.a)[amenity=', @amenity, '];way(area.a)[amenity=', @amenity, '];rel(area.a)[amenity=', @amenity, ']; );out;'),
       NULL, 10000, 0, 0
      ).value('/Response[1]/Body[1]', 'NVARCHAR(MAX)'),
      '$.elements'
   )
   WITH
    (
      [type] nvarchar(max) N'$.type' ,
      [id] nvarchar(max) N'$.id',
      [lat] nvarchar(max) N'$.lat',
      [lon] nvarchar(max) N'$.lon',
      [amenity] nvarchar(max) N'$.tags.amenity',
      [name] nvarchar(max) N'$.tags.name'
    )
);