A real straight-forward and simple guide for a few free gems here and there.
Click the Water fountain in the rear.
The PVP Arena
Click one of the street lights.
PVP Arena: 5 gems daily! Though it said in game, it's worth pointing out that the daily replay in this area (the TV in the street) will give you 5 gems a day.
The Card Shop
Click the top of the shop, above the doors.
The Card Studio
Click the trash can in the bottom left.
The gems aren't daily, they're random. I've seen as few as one, and as many as five so far. The spots are the same in regular and GX, be it PC, Android, or iPhone. Have fun!