Current Internship Advice

I started my internship this summer and I am starting my third week now. I am just confused about the dynamics and would appreciate some advice. I pretty much never have work to do and really only get one task a day that only lasts about 30 minutes. I don't want to appear as if I am not being productive but it has been a while now and I am running out of things to look busy with. What are some suggestions of acceptable hobbies/tasks to fill the day up with when I am not being given intern work (we don't have a summer project)? In addition to this, I stay until like 9:30 to seem available as I don't want to make a bad impression, but I have never been given work past 6:30, and at this point, it just seems stupid in trying to make a good impression because then the firm has to pay for GrubHub or an Uber despite me not adding value to anything. How do I manage this dynamic of asking to leave / just leaving when I don't have work to do? As a full time, would you think negatively of an intern leaving around 7:00 if they haven't been given work / know they won't be?