All of the above comments are correct. Be cool, walk with confidence.
I'll add, as long as you're not making any kind of scene, you're quiet and look amicable, then no one will pay any attention to your activities in the hotel. I once got stuck waiting on room number, so I parked myself right in the lobby in a chair in full view, played around on my phone, then made an exasperated face as I went to the elevators, as if I had forgotten something.