I'd upvote this many times, if I could. I got in the habit of doing several hours of work a week at the library while my kids were doing various activities, and I loved it. At first, I did have that "gee, am I just taking space" moment, but just as Thomas points out, this is actually what libraries are for--they provide knowledge services (that is, books and internet access) for free.

I'd also recommend that if you do use your local library, support it, too. I don't necessarily mean monetarily (which we do, via, uh, late fees), but if someone in power is considering cutting funding, tell them they really shouldn't do that.