explain select * from zipcode_distances z inner join venues v on z.zipcode_to=v.zipcode inner join events e on v.id=e.venue_id where z.z
You could use a subquery:
select * from zipcode_distances z, venues v, events e where z.id in (select id from zipcode z where z.zipcode_from='92108' and z.distance <= 5) and z.zipcode_to=v.zipcode and v.id=e.venue_id