Possible internship topics for a second year undergraduate student interested in astrophysics
Yay, astrophysics! That's my field, too. ^_^

I would focus less on what topics you could work on and more who you could work with. 

For a research position, I'd suggest asking your physics and/or astronomy faculty if they have any research you can assist them with. This is a fantastic place to start, and it's where the vast majority of astrophysics people get their first research experience. In my experience, these positions are usually paid, but I know of situations where undergrads informally volunteer (and work fewer hours) in order to get the experience and extra advising. If your institution doesn't have any options, see if there's a college or university nearby that does. 

You can also volunteer with your college or university at astronomy and physics outreach events. You can also see if there's an observatory or astronomical association near where you live, and see if you can't get involved there. You may find some paid part-time positions through the connections you make there. 

For an internship, you can look for astrophysics-like businesses near you and see if they have any openings. There aren't many businesses that specialize in astrophysics, but there are many aerospace businesses. If you're open to looking at any of these, you may find luck.