There are a couple of different ways to do this - if I were in your shoes, I'd get a repeater box. A repeater gives you a twofer - 1) you get a local connection you can run a wired device from, and 2)you can use it to extend your wireless network's range or improve its signal quality. Repeaters (also called WDS, or Wireless Distribution System boxen) are made by most if not all of the wireless network manufacturers (Cisco, D-Link, Hawking, TrendNET, Netis, etc.). In addition, many of these are simply re-purposed access points - if you get one of these repurposed APs (some are quite inexpensive,
Caveats about using this method:
1) Not all WiFi repeaters have an RJ-45 cable connection, and even if they do, not all enable it when in WDS/Repeater mode. Check carefully with the mfr. before buying.
2) When in WDS or Repeater mode, if the box in question does not have MIMO (multiple-in, multiple-out) radios, then creating a repeated network will potentially cut your wireless clients' throughput in half. Again, read the specs carefully before choosing.