Seeing as there are no other responses, I figure should chime in and lend the biggest helping hand I can (which isn't much). I went to the rival school on the other side of the Bay (Cal), but it's in the same general area, so I'll tell you what I learned from my experience in the Bay Area. I don't know what level of cost-of-living you're used to but I can tell you it's more expensive than LA, but cheaper than NYC.
I also don't know if Stanford offers any student housing opportunities for graduate students or not, because otherwise, housing is really variable depending on your preference. If you share a room and are willing to commute, then it can be affordable. Otherwise......good luck, because even for the cheapest accommodations, you'll still be overpaying. In terms of food and entertainment, it's more expensive compared to most places in the US. You'll struggle to find cheap fresh fruit and produce. Eating out will be expensive unless you're willing to go down a few notches in the health safety scale (but! if you are, that's where all the best food is!!). Utilities, you'll find that certain companies will have a monopoly in your area so you'll be forced to pay their exorbitant rates. For me it was PGE and Comcast. But, despite all these faults, the Bay Area has been my favorite place to live. I miss it every day.
I can also tell you that I also did a long distance relationship at my time at Berkeley, but I was unable to save the money for flights. Because in the end, I wanted to enjoy myself in the SF/Bay Area and go out, shop, and eat out. BUT, if you're willing to trim down these spendings, it should be possible to save the money.
So on that bombshell, yes, if you're willing to sacrifice some luxuries and can find the time in your graduate studies, you can fly out every other month-ish to see your SO. Because in graduate school, it's not so much whether or not you can afford the money, it's if you can afford the time.
And please don't kill my alma mater at the next Big Game.
Hopefully my drunken ramblings can provide some insight.