The office was rented, because I can remember Cordy complaining a couple of times about the free clients not helping to pay the rent. On the other hand, he did buy the Hyperion a couple of seasons later, so he had a source of money from somewhere. And no, I'm not forgetting the valise fll of cash that he found in the basement. There might have been enough money in there to buy a house, assuming that the silver certificates were still legal tender after all that time, but a hotel, even a long abandoned one like that, would require a down payment ranging in the high six figures, even before the required renovations and utility hook ups were made.
Maybe Angel found out about the treasure chamber in Sunnydale, where Spike found the the Ring of Amara, and took some things from there.