If you live by yourself, you're looking at VERY steep rent (I'm living in a 1b/1ba and I'm at $1100/month). Apartment complexes that have studios start around $1000/month. Once you opt to live with others, then rent will significantly decrease. Most apartment complexes at most cover hot water. Everything else is out of your pocket.
UCSD also has affiliated housing for grad students/staff/etc.....there are waitlists for these, but you could consider looking into it (http://hds.ucsd.edu).
And I don't agree that you have to be on the west side of the 5 to bike to school. I know plenty of people who live on the east of the 5 and bike to school. I'd say if you live anywhere accessible to the free student shuttles mentioned above, you can bike it, too.
There's a Trader Joe's, a Whole Foods nearby. If you can go further (i.e. if you end up w/ a car) there's a Henry's Market Place, too.
Estimating...I live by myself, I spent maybe $1500-$1700 a month on everything (rent, food, utilities, etc) combined.