I lived in Irvine for 4 years as an undergrad, it's not the cheapest city in the OC to stay in. If you're looking for slightly less expensive housing in nearby cities, try looking Tustin, Costa Mesa, or Santa Ana.
If you prefer proximity, there's a couple of apartment communities right across the street from the school: Dartmouth, Harvard, Stanford, Columbia, Oxford, and Ambrose (don't ask why they're named like that). They're the clusters of apartments between campus dr. and university dr. I lived in one of these for 2 years with 3 other roommates and my rent was in the $500 range per month.
Apartments slightly farther from the school (and slightly cheaper): Woodbridge, Parkwood, Park West, Turtle Rock, and Rancho San Joaquin.
There's 2 apartment places that I think the school has a deal with so they only do UCI students/faculty/affiliated: Vista Del Campo and Vista Del Campo Norte.
All of these places are north/east of the university. If you go south of the school, you're quickly in Newport Beach and you don't want to be paying those rates.
Also, you need to have a car to get anywhere in socal. If you don't, at least have a bike to start off, there are some nice bike trails in Irvine.
Overall Irvine opinions: it's nice. And sterile. The good thing is, OC is full of really good food, and Irvine itself is incredibly safe (the Irvine police will ticket you for jaywalking, they really don't have much to do). A lot of (upper middle class) families are here to raise their kids. Honestly, the campus is really beautiful (there's a huge park in the middle of the school, great place for a nap in the spring or summer... well you have time to nap as a grad student haha) and bike friendly. There are great beaches around too, and it's close enough so that you have access to everything in LA or San Diego if you want to do a day trip. Oh yeah, Disneyland, there's that. Good luck on your search.