Hi Harvey,
This is just what I would do, so I didn't need to buy a bridge: I'd turn one of my machines + the router into a bridge. I had a setup like this in my workshop all last week while I was working on my printer power control circuit. I used Linux on my "bridge" laptop and you'll be using Windows, but the general ideas are the same. I just might miss a step or two since I'm a little rusty on the Windows side of things. :/ I *think* Windows XP and Vista can both do this. I know Linux can.
I'm just going to write this out as if it was a HOWTO since I get tired of writing "I would do *this*, then I would do *that*, then I would do *something else*. . .".
Pick an existing computer which has a built-in NIC. If neither does, buy one (they're cheap) and install it and the Wifi adaptor in one desktop.
Connect to the city's access point using the Wifi adaptor. If the signal is too weak you can get or make a higher-gain antenna and use that in place of the stock antenna on the Wifi adaptor (assuming that it has removable antennas with standard antenna jacks). You can use something like
Netstumbler (free download) on Windows to check signal strength.
Configure the Ethernet NIC to have a static address of, say, 192.168.0.100. Give it a netmask of 255.255.255.0. Put the city Wifi access point's IP address into the gateway field. Plug it into port 1 on your Wifi router. In your web browser, make sure that you can connect to your Wifi router's configuration page.
At this point you should be able to connect to your Wifi router from other local computers either by plugging them directly into the router's other Ethernet ports or wirelessly if they have Wifi adaptors. On your local network, the bridge computer's IP address will be 192.168.0.100. Other local computers should be able to ping the bridge computer at 192.168.0.100, and the bridge computer should be able to ping them back at whatever address the Wifi router has given them. However, only the bridge computer at this point should be able to ping the city Wifi access point or access the Internet.
On the bridge computer, go to Network Connections and simultaneously select the Wifi adaptor and the Ethernet adaptor (make sure they both say that they are Enabled first). Right-click on one of them and select "Bridge connections" from the popup menu.
If all goes well, after this, the local network computers should be able to talk to each other and also access the Internet. Traffic from a local computer will be routed first to the Wifi router, then via Ethernet to the bridge computer, then via the bridged connection you just created to the Wifi adaptor, then wirelessly to the city Wifi access point.
Unfortunately I don't have Windows running on the machine I'm using right now or I'd test my assumptions on what Windows can do, but I think the above should be just about right. I know that it was easy to set up the laptop to bridge its Ethernet and Wifi connections so that I could plug in my cheap old Linksys router here in the workshop and make a local Wifi access point with Internet access and local networking.
OK, I know that was long-winded, but it's really not that complicated, and it means that you should be able to skip buying a bridge. Of course, there may be aspects to your systems or city Wifi which mean that some things would need to be changed, but this is how I was able to do something very similar.
Note that you really should also enable the firewall (ideally, install something like ZoneAlarm, but the Windows firewall can also do) on the bridge computer to protect the local network.
Hope this helps,
Torben