The value of a pre-application visit is debatable, and depends on the school. Some schools encourage it and some strongly discourage it. But once you've done your faculty research and know enough about your POIs to make serious inquiries or have relevant questions, if you feel confident enough to get in touch with them about your interest in the program, and if they respond, I don't see what the harm would be in asking if you could meet up in person, or speak on the phone, etc. I think it would be a bad move to just show up, not because it's presumptuous necessarily but because it could be rather intrusive.
Also, I can't guess your gender, but if you are a woman I would highly recommend not telling the program that you hope to attend the school due to proximity to your boyfriend. Academia is wary of married women and women with children, and I don't think citing your boyfriend as the cause of your interest in the program will do you any favors. (Not that there is anything wrong with your choices, just that even the most educated people were raised in this patriarchy and institutional bias prevails.)
Slate article on the pay gap/tenure gap of women with kids here.