If you've got a crawlspace available that's probably your best bet. Hardest part is hitting the stud cavity. You can usually tell where you are by looking for nails sticking through the subfloor where they attached the studwall to the subfloor and/or looking for existing cable runs going up through the subfloor.
From there you'll have to drill a pilot hole to make sure you can hit the mark. Then another big enough to run a fish tape up through and make a trial run to make sure there's no obstruction (fire blocking, insulation, plumbing, ect getting in your way. If you have two people it's best to have one person fish and the other upstairs seeing if they can hear the fish tape scraping the inside of the wall.
Then mark out you studs with a finder, mark out where you want your outlet to go, and use a hole saw to cut out your box location. Find the fish tape, then pull it back down, tape the cable to it and run it back up. Pull it out the hole you cut in the wall, tape it to the wall so it doesn't run away from you, then feed it through an old work or low voltage box, stick the box in the hole you just cut, then anchor it down with the dog ear flaps that flip out when you screw it down. If it's a short run you can just use a pre-made 50 foot coax with pre-terminated ends and screw it to the back side of a cable outlet plate. Then screw the plate to the wall and terminate the other end to the splitter or whatever you are using to distribute out the signal.