live in the house that is used for the office?

Is the house where Welby and his wife lived? I cannot find any info on the back story and I have not watched all the episodes.

It's a great question and there appears to be no detail on the show, on the internet. My guess is the house where the office is is Welby's home, and Kiley lives elsewhere.

I sometimes used to see this show on the original run, and ISTR he lived in an apt.

Coming to work on his motorcycle, I don't think there's much doubt that Dr. Kiley has an apartment elsewhere.

If I had to guess I would say that Dr. Welby resides in a house of his own elsewhere, I'll have to start re-watching episodes to try to confirm that.

I think Kiley did live there for a while, or at least in the first season. The ep where he gets chicken pox (S01E21) he comes down the stairs in the morning in pajamas and hair mussed and complains to Marcus how he didn't catch any fish and thinks he got bitten by mosquitoes indicates that. He also eats lunch there with Marc that Consuelo makes occasionally. But I agree that eventually he gets his own place and then digs with Janet after they are married.