We are now using a geocoding solution with real address suggestions. Based on photon.
If you search for a location on openstreetmap.org you’ll probably miss some autocompletion. Autocompletion requires some server resources and when you have a normal SQL database (as it is the case for normal nominatim installation) this is nearly impossible. There is an Open Source solution called photon using the nominatim DB for feeding and for the search it uses Apache Solr. I highly recommend looking at this.
BTW: Maybe you have some time to use this into the latest effort that wants to have routing on the main osm.org site? Check this fork!