a day and a half in Israel - Jerusalem only or Jerusalem + Tel Aviv?

I second catw's recommendation of the Austrian Hospice. Be aware it gets booked up months in advance. An alternative is the Christ Church Guest House, just inside Jaffa Gate or, outside the old city but within walking distance and in a prime location just opposite the King David Hotel, the YMCA.

Yet another alternative is the Lutherian guesthouse near Jaffa Gate, inside the Old City.