What a good app to tag my favorite places?
Google Maps does indeed allow this.


Find the place you want.
Bring up the details for that location by tapping on it, either in search results or the box at the bottom of the screen after you have selected a place.
Tap the Save icon (between Call and Website, highlighted in the screenshot).


These places are included when searching going forward, as well as displayed on the map view with gold stars when you are sufficiently zoomed in.

You can also view an overall list of them by tapping the  menu, selecting Your Places and scrolling to find your Saved Places.