indexing lat lon

I have the following situation:

I'm developing an reverse geocoder, so input is lat/lon coordinate and
output is the nearest textual location.
I have a database of +- 2 000 000 records that contains lat/lon and full
name of the location.

These are the steps I take now:
1 'draw' a box around the lat/lon position we have as input
2 search the DB for all the points in this box
3 measure the distance to each point in the box

This works fine, but step 2 takes too lang for obvious reasons...
select * from table
where lat between box_point1_lat and box_point2_lat
         and lon between box_point1_lon and box_point2_lon;

This would require a seq scan for but indexing the table doesn't help much
either (factor 2) ...

Is there a good way of indexing the lat/lon column so lookup is faster? I
have looked at PostGis but didn't think it would give a good solution in
this context (correct me if I'm wrong)

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