My old android phone is 6" x 3-1/8". I have a small wristlet which fits it perfectly and has 2 card slots. I use that as a wallet. The phone will also fit in the back section/pocket of my pennys and ramblers legacy bags.
I recommend just getting a wristlet to fit it. When you have a bag with a big enough pocket, you have the option of putting it in there by itself, or just putting the wristlet into the bag.
Try the wristlet with the phone in person, though. Mine is a tight fit.