Help with internet filtering

Hello,
I would like to request assistance in trying to solve this problem.

Problem statement:
I have a wireless Internet connection at "Public Location" (PL), however, most of the websites are blocked which is sometimes very annoying and slows me down.

Goals:
To gain unrestricted access to the web via Internet Explorer

Setup:
I use my personal laptop with a wireless card to connect to the network and Internet at PL. I also have an Internet access at home. My home network consists of a Linksys WRT54GL router and 2 desktops with wireless cards.

What was done:
Network at PL is configured the way that it will not allow me to connect using windows standard Remote Desktop connection. However, I've found a way around it by running TeamViewer software on my laptop at PL and a desktop at home. That allowed me to achieve the same thing as remote desktop connection would. The downside of that is that the desktop movement is choppy and the images are appearing with a delay. All that is attributed to the lower connection speed compared to LAN. I also tried configuring IE to connect to a public proxy server with no significant improvement. Most of them either don't work or are very slow. Now they have blocked the TeamViewer also and I cannot connect using that either. Also, using https://www.vtunnel.com for now untill I get a more permanent solution.

Possible solutions:
An ideal way to resolve this would be to somehow configure my router to act as a proxy server of some sort. That way when I'm at the PL, I can connect to it directly and access the Internet through it.

A less desirable way is to run a proxy server on one of my machines at home, but that would mean it has to stay on all day and it would increase my electric bill which is already high.

I'm also open to any other solutions, so if you see a way to resolve this even better, don't hesitate to comment

Yeah, and the question is, how the heck do I beat it?