What you want to do is to order the results by distance, ascending, then limit the output to ## results. (The SQL should show ORDER BY distance ASC LIMIT ).
For this kind of very custom request, I'd probably simply make a small module with a page that took everything from input boxes as arguments instead of filters. I'd grab the query from the views interface (so I didn't have to figure it out myself) and change it into a SELECT COUNT(*) type query, and then write some simple code in a loop - checking the result, and if it's suitably large, exiting the loop and then using those parameters for building the view. This should save you a lot of time compared to trying to figure out how to do it with all the various options in the views builder widgets.
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