It is possible that you can get your POIs to display on an APP. running on your Android Phone, do you have a file that contains the POIs ? If so what format is the file in ? eg :- a GPX file
If you want a new GPS unit then even the very basic GPS unit can have POIs (Points Of Interest), these Points are also called Waypoints or Favourites, The Garmin Products probably start with something like the Etrex SE, this will store 50 Waypoints, however the Maps it can store is limited so you might want to choose a unit that can have more detailed mapping