The way I would accomplish that is to change the sshd config on the host being connected to, and allow x-forwarding, which (wisely) is turned off by default. Then when you are ssh'd into the server, just issue a command like konqueror, or firefox (no ampersand at the end), and it will appear on your local machine, but will be running off the remote one. This will allow you to connect to things on local IP networks to the remote server.
To ssh in with X forwarding, you need to issue the command on you local machine
ssh -X my.server.org
Doing this is of questionable value, as servers should not have GUI wasting their resources. Even though the X system doesn't run on the server the way it does on a desktop, you still eat system resources to simulate it. Furthermore, learing your way around a system through the command line interface (CLI) not only puts the proverbial hair on your chest, but gives you portable skills that aren't dependent on junk like the window dressing (ie someone saying, "I can do this in Gnome, but not in KDE"). When you can accomplish things from the command line, you can accomplish them anywhere, reagardless of the window dressing over the top.