If you need a good task and todo manager that integrates right with the GNOME desktop, Getting Things GNOME may be the right choice for you. Gnome developer Baptiste Saleil recently posted some screenshots of the progress he made in integrating integrating GTG with GNOME shell. It looks awesome.
You can now search your tasks right from shell search bar, and also edit them with a single click.
If you click on calender on top, all your upcoming tasks of today and tomorrow will be displayed. Smart!
Also the calender menu has a nice todo list, right of upcoming tasks
All the above is done by a few gnome shell extensions which are configurable to your needs
The developer also wishes to build a notification system soon. Can we finally see a fully integrated todo and tasks management app in GNOME shell?