I am looking for a diplomatic way to tell someone that I would love for them to come visit, but they can't stay here.

My friend has a giant house with four floors. I have a tiny tiny 450-500-sq foot apartment with one small bedroom and a toilet that refuses to work on regular intervals.

My friend wants to come and visit, which is very nice of her. She wants to stay for four days and three nights. We found a weekend that works and she said "so should I bring a sleeping bag?"

I responded that my entire apt would fit in her living room and that one night would be fine, after that she would kill me and my cats who like to smash things at 3 a.m. I said I'd be happy to split the cost of a hotel.

She wrote back - oh I'm sure I can just sleep on the couch.

Except no. I really, really don't like having people in my space. I need quiet and alone time. It stresses me out immensely to have people over.

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What can I say that is not rude?

UPDATE: She is now saying that we can spend a day with me "Showing her the big city!" I live 75 minutes from the big city (Kansas City.) I have never been there except to pick people up at the airport. Man, I have a feeling this is going to be very bad. What's really sad is that she is one of those very pragmatic, unemotional people. She would not understand why this is stressful to me at all.

Update part 2: I found a hotel at a great price. So she would have to pay $120 to stay and I would pay the other $120. *Let me add that she earns significantly more than I do. * I said that my place was just too small for two people and that it was a really bad experience when another person slept over because we were on top of each other. (not in a good way.)

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She wouldn't do it. I might be moving in June to a slightly bigger place and she said she would wait until I found someplace that would accommodate her frugality. I feel awful because it was very nice of her to offer to visit, but at the same time, she HAS to stay with me to save $100?

I'm a middle-aged teacher. At what point is it OK for me to set boundaries and say no?