I have yet to see a single device that would extend as well as pick up your city WiFi.

However if I wanted to attempt to solve this I'd use a pair of devices (items follow) and configure them as follows.

I'd get a WiFi client device such as this one.
-> Setup is just a normal client setup. I won't duplicate or write further.

With the WiFi client working I'd get a WiFi router such as this one.
Or another from http://www.amazon.com/Best-Sellers-Electronics-Computer-Routers/zgbs/electronics/300189

This second router is this configured as a WAP or you can try plugging the WiFi Client into the Internet port.

-> Placement is critical here. You want the Client to be where it can pick up your home system and the second router provides a new WiFi zone.

About 135 bucks total to setup.