We used an unknown at a clinic, so this is not from personal experience, but more from what others have done...

Most people do it at home, their home. And the donor comes over, maybe for dinner or something, and then he can go into the bathroom or where ever you've agreed on, and do his deed, and then he gives it to you, goes home and leaves you both to it.
(Possible TMI ahead...)
I think your home works best as it obvious gets fairly intimate. Because its only vaginal insemination and not an IUI like at a clinic, its recommended that you get aroused as the bodies natural lubrication is good to help the swimmers get to where they need to be, and an orgasm helps the cervix dip down into the semen and again get the swimmers to where they need to be.

Sorry to be so graphic LOL! But yeah, people like to do that at home because then they don't have to move afterwards. No idea if that actually helps, but a lot of people prefer it.