Obviously the best solution would be a hardwired network. If you have a basement in your 2-story house then the main issue is finding a way to run wiring from the basement to the attic. You can drop cables from the attic to any 2nd floor room. From the basement, you can go up through the ceiling for the 1st floor. The trick is to find a way to run wires between floors.
I have the exact same scenario in my house and I was able to create a raceway between the basement and the return duct for the A/C system that was basically an empty space behind a wall on the 2nd floor. I just cut an access panel from my master bedroom into the return duct area and was able to find a spot that allowed me to drop wires from the 2nd floor to the basement ceiling, although I had to drill a few holes in the floor and ceiling. Once I had a clear path I widened the openings and dropped a long cord through the raceway with plenty of slack which I then tied off at both ends. I just pulled the slack through from the other end, attached my cable, and pulled it up through the wall to the 2nd floor. From there I could easily feed it into the attic and then route it to whichever room required it. I located the frame above the wall and drilled a hole through the 2x4 between studs and dropped the wire through the hole. I cut an opening in the wall where the wire was dropped, installed a low-voltage outlet box (basically just a plastic frame that clamps to the drywall, available at any home supply store), and attached the cable to a wall plate. I connected the cable to a network switch/hub in the basement which also connected to my router for internet connectivity.
Note that if you have a finished drywall ceiling in the basement you will probably have to create an access panel in the ceiling to allow access to the location where the wiring drops from the 2nd floor. I have a drop ceiling in my finished basement that I put in with the knowledge that I'd need to have access to wiring in the ceiling. If you don't have a return duct or other vacant space behind a wall on the 2nd floor a closet will work equally well. You'll probably want to set up some sort of conduit between the closet floor and ceiling to protect the wiring.