HGUser, PostgreSQL and SQL Server (2008 onwards - 2012 is best) are both great options that meet your requirements. Both support FULL TEXT searching and Spatial Queries with Indexing (either as singular or combined WHERE clauses).
Just make sure to construct a geography / geometry object from your lat / long coordinates to benefit from the Spatial indexing.
For PostgreSQL
You can read about Geography / Geometry within the User Manual at
http://www.postgresql.org/files/documentation/pdf/9.3/postgresql-9.3-A4.pdf (section 8.8)
And Full Text will be found at Chapter 12 of the same document.
For SQL Server
You can read about Geography / Geometry at
http://technet.microsoft.com/en-us/library/ff848797.aspx
And full text indexes at