Using extension cables for WiFI is not something you want to do, particularly linking them together. At WiFi frequencies there is a lot of loss in connectors and cables. The bigger antenna will help a lot (and with a USB adapter, generally output power is about 80mw so you will still be within FCC specs) but realize the extra gain comes at the cost of coverage off the plane of the antenna. That is, an Omni collects and emits power in a "donut" shape with it's axis perpendicular to the antenna mast. The higher the gain the "flatter" the donut, so you may be able to pick up much further straight out from the antenna but not something sitting above or below that plane. I also seriously doubt the antenna pictured is anywhere near 16dBi. Professional omni's run up to about 12dBi but gain=length (in general). That one may hit 6dBi, but not much more.
As for your cable, if you really, really want to do this, get the right length cable with the right connectors. Every connector costs quite a bit of signal loss at 2.4Ghz. Remember 3dB is half of your signal, 10dB is 90%. Go someplace like Streakwave.com and get low loss cable, like LMR400, in the length you need. Just the cable, at 60', is going to cost you a bit over 4dB plus connector losses, so your 6dBi antenna and cable now equals your 2bBi antenna.
If it were me, I'd look at getting something like a Ubiquiti PicoStation (or use a Loco and get the advantage of a directional high gain antenna) and put it where you need the antenna, and run Ethernet back down to your local switch and connect that way. Use outdoor rated Cat5 to connect the radio if you go outdoors on the run - you will be kicking yourself in a year when weirdness happens if you don't. This setup gives you a much more powerful radio and decent antenna with effectively no loss down to your PC. If there is more than one Ethernet device on your local network you should set the PicoStation (or Loco) up as a router (or connect it directly to the "uplink" port of a router) so multiple devices can share the connection. Several other outfits (Mikrotik, Engenious, and others) make similar radios, I just happen to be most familiar with the Ubiquiti.