Yeah it's usually much better to try and boost the range of the existing wifi unit (with better antennas), or make a wired run to the other location and install a second access point there. Repeaters tend to exaggerate interference problems, and greatly lower available bandwidth.
^ Yup. A higher gain antenna will, generally specking, "throw" the signal further, but with a beamwidth trade-off. For a regular omnidirectional antenna, image a donut surrounding the antenna. That's how the signal tends to propagate from a typical omni antenna. A higher gain omni-antenna would propagate more like an 18" pizza crust. It reaches further, but the width is much narrower.
Now, you *could* always get a 1 watt amplifier, and buy an adapter, and a pre-fabbed piece of LMR-400 coax, and buy a large 8db omni to mount inside, but that's like using a sledgehammer to swat a fly, and it greatly increases how far your signal
propagates, and *could* allow an intruder to have fun at your expense.
Some of the easiest things to check would be:
1)run Netstumbler in various areas to see exactly where the signal starts faltering. I haven't run the tool in a while, but it would show every SSID being broadcast, all the channel usage, and your SNR to/from the AP. That info will aid you in deciding if moving the AP, getting a high gain antenna, or even getting a WiFi card with better Tx/Rx sensitivity, before grabbing AMPs and such.
2) Placement of the WiFi unit. How the walls are constructed matters. Different materials reflect/absorb 2.4 and 5Ghz signals. Wood, metal, brick, cinder blocks, all those affect the signal. Can you move the AP to better or more central location?
The upcoming 802.11ad (WiGig) is going to be even worse and it'll only work within a room.
3) If worse case, try to get a system that'll let you use sectorized antennas, and aim those at the areas you want WiFi only.