She's informed me that she will protect me with her life and whatnot, but I'd like to adventure by myself for the time being. Is there a place you can send her to or you just order her to wait and leave?

Just tell her to "wait here" wherever you want. I forgot her with the greybeards on high hrothgar.

Cool. Guess I'll have her stay at Riverwood.

That's a neat idea. Thanks.

Well after 1 incident when she murdered me because I accidentally set her on fire, I told her to stay in Whiterun.

That and I'm horrible with companions. I killed one, I let another one get murdered by a bunch of people in a fort and I set fire on Lydia.