You could try a Wireless Repeater device. I suggest a D'Link wireless repeater. Don't worry about the price, since they do their duty as wel as possible, so go for the cheaper one.
Or buy another better antenna.
The idea with the repeater is nice, but it'll have to be powered and in the range of the WiFi, so you'll have to convince a neighbour that receives the signal to put the repeater in his house