Extending Internet to detached building
Keep in mind that the feedline (coax cable) going from the access point to the external antenna will drop your signal strength. Here's a good quote from SuperUser on this topic:

"A common relatively inexpensive cable for short runs of WiFi antennas is LMR100. At 2.4 GHz (the common WiFi band), 15 feet of LMR100 will result in signal loss of about 6 dB. That's equivalent to dropping power to just 25% of what it was. (Each 3 dB = 50% gain or loss in power)"

If it looks like you would have to run a long feedline, an alternative is to use an outdoor access point. You'd place it on the outside of your garage, set it up as a wireless client, and wire it with ethernet to the access point inside the garage.