One of greatest things about Postgres is its extension system which is meant for things like this. RDS not supporting custom extension is RDS problem and frankly I wouldn't recommend using RDS. You are losing a lot of functionality, upgrades are tougher etc. Postgres maintenance is quite low the hardest part is probably running and RDS doesn't save you from that.
Anyway this feature discussed (searching based on a distance) is part of PostGIS extension they are demonstrating here SP-GiST index.
Anyway this feature discussed (searching based on a distance) is part of PostGIS extension they are demonstrating here SP-GiST index.