There are many pool halls in the Evanston area (but not necessarily in Evanston itself). I grew up in that area and know it well. Chris's is about a 20 minute drive and is right off of 94/90 pretty much at the corner of Lawrence and Milwaukee Ave. They have about 45 tables there. Not too far from that is the Chicago Billiard Cafe on Irving Park Road. They have a huge tournament on Thursday nights (one of the best paying ones too). There are a few places in Rogers Park which is right next to Evanston, but be careful because parts of Roger's Park are real rough especially near Loyola.
If you do have a car, there is a very nice pool hall in Glenview called Premier. They are kind of expensive, but they have a full service bar, the tables are super nice, and the room is incredibly clean.
Lincoln Billiard cafe is nice. It is on the north side of Chicago in the Lakeview area. The tables are ok, and there is no liquor there.
City Pool Hall on Hubbard is really nice. The tables are in great shape, they have a full bar and a full kitchen.
Pro Tyme is a beautiful room, however, it is a long drive from Evanston. Without traffic it is 45 minutes to an hour. With traffic, it could take 2 hours.