I loved how much my boss trusted me to complete tasks with minimal guidance, including leaving the office to attend reading of new work and writing coverage on them.
What I wish was different
I wish I'd had less down time; I think I didn't coordinate my work with my boss's schedule well enough, so there were many days when I sat around waiting for her to be free to meet and debrief work or assign a new project.
If you want to try something new, just ask! Or if you want to sit in on a meeting that sounds intriguing, just ask. The people in the office want you to learn.