Downtown Kansas City, especially the Westport area, is full of hip little coffee shops where you can stop in to rejuvenate or hang out all day. Here I will give you a brief account of the more popular coffee shops in Kansas City.
Westport Coffee House is a Christian ran coffee shop located on the corner of Pennsylvania Avenue, right next to the Beaumont Club, down the block from the Kelly's. Their coffee selections are average, offering a variety of flavored coffees and blended drinks, but they do feature several arcade games such as pinball and a Pac Man table. They also show art from local artists, but their shows are notably less impressive than other coffee shops and especially galleries nearby, so don't go just for the art. Their open mic and poetry slam nights are nice gestures, but just as unimpressive as the art they display. Occasionally, they will hold concerts and shows in the downstairs part of the building. The shows put on here are usually good, and the performance space is great for lots of different "unconventional" performances. I usually go here because a) they have their own huge parking lot, which makes for an easy in-out process or b) for the Pac Man table. They also have computers that you can pay to use and a jukebox.
Broadway Café is located on Broadway just past the Country Club Plaza. This place is usually frequented by the art institute kids and local scene kids. The art they feature is hit and miss, but the ones they hit on are usually very good. One of the things that makes them different is that they offer vegan snacks such as granola bars, scones, and cookies. Their coffee is good and pretty cheap, with about the same variety as WCH. However, they do have several bookshelves in the back where people are encouraged to take and leave books as they please. Also, the outdoor seating is great for people-watching.
My favorite place is the Crave Café, located on 39th St. just a couple blocks before Broadway. This is an old house that someone bought and turned into a coffee shop. There is an upstairs level with three rooms (all smoking) full of chairs, tables, and couches where you can read, play checkers, write, do homework, or simply meet new people (imagine that!) and talk. The downstairs level is similar, with three different rooms besides the front room where coffee is served where you can sit and read. The Crave Café also has a book exchange collection. Their art exhibits are mysteries; sometimes they will have whole collections up by the same person, sometimes they will have nothing up, and in some places they have art for sale that has been there for years. The art here, like at Broadway, is hit and miss. The owner of the Crave is usually working during the daytime, and he and the employees are usually very nice. There is also a large front porch to the house with lots of tables and chairs.
Whatever atmosphere, availability, or scene you are looking for chances are that you can find it in one of these coffee shops, if not one of the many others nearby.