A wireless bridge can work if the signal is strong at the point where you place the device. An inexpensive dd-wrt capable router flashed to the dd-wrt firmware does a great job IF the signal is good at the distant location. A pair of the new ASUS AC66U is quite expensive but works very well with one as the primary router and the second in bridge mode.
Rather than a cable you can use either your electrical sockets (powerline) or TV coaxial cable (MOCA) to bridge the distance instead of a cable. Main router --> powerline or MOCA adapter --> internal home wiring --> 2nd adapter --> second router configured as wireless AP.
Powerline is cheaper, but slower and you need to buy the adapters from somewhere you can return them in the event that your home wiring doesn't work well with them.