I used to live in Evanston and can offer some advice, though it's been a few years since I was there. In general, Evanston is more expensive than the Chicago neighborhood of Roger's Park, which is just south of the Evanston border but still quite accessible. The further north you go, the more expensive it gets, though it also gets cheaper as you get away from Lake Michigan. Transportation can be a big expense anywhere, so trying to get close to an El station, and even better, both an El and Metra station at the same time (think Main St. or Davis St.) would be an excellent move. For groceries, try to scout out ethnic markets in Chicago and Skokie. If you travel a lot, maybe try to be close to a bus line that heads to O'Hare (there use to be a direct bus from downtown Evanston - maybe it still exists. For fun, get a bike and head to the lakeshore or the forest preserve trails.
One hidden gem I should mention - be sure to visit the Baha'i House of Worship located just north of Evanston in Wilmette for an example of stunning architecture situated in a beautiful garden setting with great views of the lake. It is accessible via the El or by bike, and is free of charge.
I hope this helps!