You would be best off just doing wireless from his garage. That way you don't have to worry about running the cable, signal strength, etc. etc. etc..
A repeator operates at layer 1, just polishes up the signal, and sends it on it's way. A a router also does this, ANY router does this. As for wireless, there are lots of wireless routers on the market. Just make sure that the technologies match up.
802.11a
802.11b
802.11g
The 'b & g' standards work together in the 2.4 GHz range, but 'a' works at a different frequency, in the 5GHz range.
The cost of getting (2) wireless routers to eliminate the cable will roughly the same as the cable.... figuring that you would need the cost of the long cable, krimper & ends for the cable, material to protect the cable from the elements, plus the actual work of installing it. But hey, if you have the cable, ends, & krimper, go for it...