I don't know SQL Geospatial new feature.
I'm wondering if I can use to make something like:
I mean can I make and app that allows you to insert delivery locations on a map and then make some BI analysis on this info?
Are the types Geometry and Geography suited for this? Thanks in advance.
You could store the point in SQL Server, and the geographic extensions can do things like handle polygons and testing the points for being in the polygons.
Without a database of state,city,etc polygon definitions, you will need a Geocoding service. Eg. One of the Bing Maps web services, or a desktop solution such as MapPoint.