Are you considering spending more time in Zion now ? The two walks you are considering are amazing, but both Strenuous and time consuming. Angels landing is not only challenging, but has steep drop offs and is not for the faint of heart and the Narrows require you to walk in the river and you will need the right gear, which can be hired in Springdale.
I would check carefully to see that your parents are up to it, if you are planning on an overnight stop. If not and you are travelling from Page AZ to Vegas then I think the best way yo see the canyon is a stroll along the 'Riverside walk' and perhaps a short walk to 'Weeping rock'.
To stay on the East side of the mountains prior to Yosemite, you could stop at Bishop, Mammoth or Lee Vining [the closest] before heading over Tioga pass. If your budget can manage a night in the park I would recommend it, if not one of the surrounding towns just outside the park on the western side for night 2.
Again depending on budget, you could stay right in the City centre of SF around Union square, or for better value within a comfortable walk to Fisherman's Wharf and Cable cars to the City, you could look around Lombard and Gough street.