best market for asian ingredients?
The Filipino grocer is still there on Clark just north of Gethsemene Garden center, on the east side of the street. I also live in Evanston, and it's a 15-minute drive. I also second the Thai grocer (Broadway/Argyle) and Mitsuwa, though that one is a hike for us. We've only been there when making the arduous trek to IKEA.
I think there is a Filipino grocery on the east side of Clark, south of Ridge (in the area where Clark and Ashland are together). I don't cook Filipino and haven't been there in ages, so I can't quite promise it is still there, or tell you much about the quality. Perhaps someone else knows more?
The best Korean market is on Kimball, just north of Belmont (right off one of the exits of the Kennedy, I believe). I think it is 3333 N. Kimball, and is called something bland like "Chicago Food".
Market Place on Oakton is good, though it doesn't have the full range. The International Club or whatever it is called on south Pulaski is simply amazing, they have everything, absolutely everything.
I second all the comments about the Argyle/Broadway area, well worth a visit, and also Lawrence/Kedzie. The Asian market I go to most often (because I am in the area) is in the corner of a strip mall on Kedzie about two blocks north of Lawrence.
Welcome to Evanston, I also live in Evanston, lots of good restaurants in the area.
Don't forget Mitsuwa the gigantic Japanese supermarket north of Evanston in Arlington Heights.
The Uptown area is probably your best bet for S.E. Asian foodstuffs[there are many, many markets---some right on Broadway within a few blocks from one another, some hidden away in the opposite direction towards Sheridan Rd.---...I'm partial to the produce at Thai Grocery(western corner of Argyle/Broadway)...but, each store has it's particular niche and/or bargain].
While you can find *some* specifically Chinese products in Uptown, I'm surprised no one has mentioned Chicago's Chinatown(red line to Cermak/Chinatown Station). Again, a plethora of markets to choose from and ingredients you won't find in Uptown...but, the same holds true that in Chinatown you won't have access to the variety of S.E. Asian produce, curry pastes, etc found up North.
Then there's Devon Avenue and Patel Bros., specifically for spices/subcontinental goodies and a great produce market just steps away.
There are also a handful of Philipino markets/buffets and possibly a Korean store or two scattered around the city. Unfortunately, I have yet to explore them.
It's been my experience there's no *one* best market. You just have to travel to whatever neighborhood and hop from store to store. Fun, in and of itself.
One reasonably nearby place is on Dempter in Morton Grove. Just drive on Dempter about one mile west of the Edens and you'll see on the right:
B.B.Q. King (inside Richwell Market)
6120 W. Dempster St.
Morton Grove, IL. 60042
It's a store and they sell some decent Chinese B.B.Q.
You might also check out the Marketplace on Oakton in Skokie. It's a great, multi-ethnic market. It doesn't emphasize Asian ingredients, so it might not fill your specific request, but you'll probably like the place.
Finally, Argyle street on the North side of Chicago is not too bad a trip from Evanston, and it has several excellent Asian grociers. If you haven't been there, make the trip both to eat and shop.