What is the best framework to use for building the GUI on a python widget?
I'm currently using gnome 3, but would prefer it to be independent of the desktop environment.
I have used the 3 following toolkits.

wxPython is a popular choice. It supports Windows, Mac and Linux but may be tricky to install on some of these platforms (that's what i've recently noticed on 64 bits MAC and Ubuntu). It has a lot of nice widgets which can be seen with the demo app that can be downloaded separately. I do recommend to have a look to this app. In my opinion, it is missing a great form designer even if wxFormBuilder seems to be a good tool. I am less confortable with Xrced which is another graphical form designer but you may prefer this one.
PySide is the python wrapper for Qt. It seems to me as a very professional toolkit. It is cross-platform as well and have a very good graphical form designer (QtDesigner). It is the best choice for open-source development. If you want to make a commercial app, you would have to buy a license which is in my opinion a bit expensive for small to medium size projects. (that's why I didn't use Qt recently)
TkInter is included in the Python standard lib and is also cross-platform. I like it very much and I am using it for my little apps. For bigger projects, i think that it is missing widgets, documentations and a easy-to-use graphical designer. If you have a little time to dive into this lib, it may not be a problem.

I hope it helps
Python Widget/GUI framework