Shameless plug: why not use H3 (https://github.com/uber/h3)?
A hex grid is the most efficient way to pack circles and is therefore the best "pixel" type to approximate radii, so simply choosing a hex size best matching the desired query radius can give you a very fast nearest-neighbor approximation.
And H3 retains all of S2's good features like hexagons following a curve (not the Hilbert curve, though) so hexagon IDs of similar value will more than likely be near each other, making range queries from a database still useful.