You can't use a signal repeater or a bridge in your case. You would have to have access to their physical connection media (meaning the cables, network and routing equipment) in order to link a Bridge or a Repeater from your home to the library. Not likely that the Network Administrator is going to allow you or help you do so, not to mention the cost in cable run would get expensive over four city blocks.
What you probably want to do is get yourself a high-powered WiFi NIC and or high-powered WiFi antenna - that will boost the range which your computer will be able to detect and connect WiFi signals. Four city blocks away is a pretty long distance to detect and connect, but this doesn't mean it is impossible. You have to keep in mind that between your computer and the WiFi access point is not empty space, there are physical barriers (buildings, walls, etc.) and interference between the signal the WiFi access point (or Router) is broadcasting and your computer which is receiving the broadcast.
I would look into getting a USB WiFi adapter which is N-1 rated, that will provide you with WiFi detection and connection capability with the greatest range on your machine. This can be more secure in that you are only giving the extended range to one machine, rather than your entire network infrastructure (i.e. with a Wireless Range Extender, you will be boosting the signal strength of your DSL/Cable modem and/or your Wireless Router - allowing other people to detect your network over the airwaves). With a USB WiFi adapter that only plugs into your machine, its just your machine that is transmitting and receiving the signals. A USB adapter is preferable if you are seeking portability and ease of use.
Example of USB N-1 device:http://catalog.belkin.com/IWCatProductPage...oduct_Id=299142
Another route you can go is to get yourself a WiFi Cantenna and see if that sufficiently boosts your WiFi signal detection range. For this to work on a laptop, you will need to obtain a PCMCIA WiFi adapter which has an external directional antenna that is screwed onto the adapter itself. Much like a PCI card on a desktop machine, there are PCMCIA WiFi adapters available for laptops which use a directional screw-on antenna. You simply screw off the dinky weak-signal antenna and screw on the WiFi Cantenna for instant signal range boost. Now because the Cantenna is an external device which is cylindrical, it is positional able and you can aim in the direction you want to detect signals. The drawback with the Cantenna is that it is external and it is cumbersome and it requires additional hardware in order to work with your laptop. However, for desktop applications it is great and with the advantage of being able to aim the Cantenna, you have 360 degrees of sight in order to detect WiFi networks in all directions.
Example of EtherDesigns Cantenna:http://www.etherdesigns.com/cantennaskits.html
One thing to remember is that that WiFi signals are susceptible to interference and signal attenutation. As the signal leaves the beacon (Router, Wireless AP) its strength is reduced over time and distance - unless there is a WiFi repeater to regenerate the signal along the path. Also, keep in mind that many WiFi Routers and AP's operate in the 2.4 GHz and 5.8 GHz - nowadays, so do many cordless home telephones; therefore, the signals from these devices which may lie within the physical barriers between your machine and the WiFi AP can and will interfere and thus contribute to signal attenuation as the signal travels from the AP to your WiFi adapter.
I would also guess that there is at least one WiFi AP within close enough proximity to your home that may be even closer than the library in your case. If it is not configured with a WEP key for encryption, you can jump on to any WiFi AP that is in range and configured for open access. Word of caution, when you are connecting to a WiFi AP that you do not control, just remember that the network traffic is able to be monitored, tracked, and cut off if you abuse it.