How do I deal with someone whose definition of friendship seems to be doing everything (and I mean everything) together?

When someone wants to join the same gym as mine, attend the same social groups/ extracurricular classes together (i.e. foreign language classes, etc.), and suggests to carpool to all these places, that takes away from my personal time and space. From reading the threads on PC, I see that even spouses are not doing everything together all the time.

With someone like that, I almost don't want to answer questions like, "Do you go to a gym? Which gym?" But since what gym I go to is not considered a private question, it doesn't make sense for me to refuse that information from her.

But when someone wants to follow me everywhere, it makes me not want to disclose even the ordinary information to her. What should I say when she asks me about my plans for this Summer again? Last time I said I don't know yet, because I haven't finalized my plan. But it's going to come up again.