The mountain setting and Y mountain are what everyone comments on and helps build BYU's brand and recognition. You just can't buy that type of signature feature for PR/brand building purposes and there it is right there next to BYU's campus.
I don't expect to see a new stadium in the next 15 years, but if they did, I say rebuild on site, in the parking lot just to the west, or the Provo High property.
A&M and others have done complete rebuild/overhauls on their existing footprint by taking one section at a time and doing it over 2-3 years. It's an inconvenience for those years, but the end result was amazing. BYU could do the same.