I understand your problem. I have a new kitten that has pee problems. The first thing I would suggest is taking the cat to the vet to make sure it isn't a medical problem. If it IS medical, usually you get antibiotics and/or change his food and it clears up. Life is good. If not, then you have to start dealing with behavioral issues. It could be a dominance thing. You may need to lock the cat in a spare bedroom, bathroom, laundry room for a few days with a litter box, food and toys and that's it. He should quickly learn that the litter box is for peeing. Also it sounds like he could have a preference for soft surfaces. Taking up as many of these as possible for a few weeks will also help him realize that he shouldn't pee there.
You might also try changing his litter. Maybe he doesn't like the smell or texture of the stuff you use. Don't get clay. It's very dusty and can cause kitty health problems. The all natural like feline pine or yesterdays news, or swheat scoop are best. Most of these have cheaper generics, even at wal-mart that you can buy.
Also try Feliway. They have plugins and spray. You use the plugins in rooms where he has been peeing but isn't supposed to and this is supposed to calm him. Also, use the spray directly on the spots where he pees. This spray tells him "I'm not supposed to pee here." The plugin and spray work in similar yet different ways so using both at the same time is like a one-two punch. I've had mixed success with Feliway but with my kitten's pee problem, it has worked. It is a bit expensive but it is absolutely worth it.
Worst case scenario, you will realize that the environment isn't the best for this particular cat and find him a home that would be more suitable for him. Hopefully that won't happen. Hopefully you will be able to work out his problems and he will fit into your house beautifully.