He literally says they have a spare room on page 25. Besides, at this point he still (somehow) thinks that Akane hates him, and that she and Himari are on good termsThanks for the translation.
It's been way too long, so I don't remember. Does Saito have money? Or is it that his family has money but he doesn't have access to it?
Asking Akane "hey, do you mind if we put your (our?) friend up at a hotel" would be way more sane than trying to keep a guest in a house that was deliberately built with no spare bedrooms.
Himari can redeem herself if she takes this chance to talk Saito and Akane into a three-way, though.