I think we'll be able to give you a better sense of your options if we get some more info your aims and on the physical layout/limitations of the room..
-- How big the room is?
-- Is the current coax exposed low on the opposite wall?
-- Do the walls/ceiling impose any limitations on pulling the existing cable up to the top of the wall cavity, running more cable around the top perimeter of the room, then dropping the new feed down the desired wall cavity (assuming you're willing to break into some sheetrock)?
-- Do you want a "clean" floating wall mount for your TV with no exposed wires anywhere (e.g., you have a conduit and power run to where the TV goes on the wall)?
-- If you don't want a cable box, are you planning on plain old analog cable, or are you looking into CableCard, etc.?
-- Furthering the last question, how picky are you about video quality?
In a nutshell, I am not familiar with any consumer solution for piping such a huge amount of data wirelessly without going to some kind of optical laser. So, you're likely going to have to get comfortable with another option.
At the cheap end, there are analog-based wireless A/V solutions that could take a composite feed from a cable box. From experience, they all tend to look terrible, and they are *very* prone to transmission interference.
Moving up to digital-feed solutions, there are just now wireless HDMI solutions coming to market, so if you *did* decide to deploy a HD cable STB on the opposite wall, you could "send" the HDMI A/V output from that box to a TV on the wall, albeit with some semi-bulky equipment on both sides of the equation. But we are talking a LOT of money, anywhere from $600-$1500+, based on what I've seen. Google "wireless HDMI" to learn more.
I think the simplest solution is just to bite the bullet and pull more coax to the "right" side of the room, either through the ceiling/walls (knocking down some sheetrock in the process), under the carpet (using flat coax cable) or around the baseboard (using a baseboard molding with a built-in raceway). I've been in your situation before, and all the technology in the world can't compete with just getting the wire to where it needs to be. It may not sound like what you want to hear, but you could spend $1000 to get a "solution" that achieves the same results of paying an electrician $300 to pull more wire. Sheetrock patches very nicely.