Coffee - the sort that is ready to drink - is available all over Japan. If you're a Starbucks fan you'll find shops in most major cities and even a few drive-throughs along the roads.
Then there's Tully's and even a branch or so of Seattle's Best. Doutor is a local brand shop as is Excelsior.
All of these offer coffee, tea, blended drinks, and food. Starbucks is totally non-smoking, but Tully's has enclosed smoking rooms. Doutor and Excelsior tend to separate their smoking from non-smoking areas by space alone so you may not get a totally smoke free atmosphere.
You can even pop into any MacDonald's for your coffee fix and most convenience storse offer freshly ground and brewed drip coffee for about 100 yen for a small cup.
And then, there are the time honored Japanese coffee shops where a cup of coffee buys you the use of a seat and table for hours on end. Don't expect non-smoking and don't look for free wi-fi as most won't have it. Plan to spend a lot more for a cup of coffee in these cafes too; anything from 500 yen to 1,500 yen (e.g., Blue Mountain, special drip through a siphon).
There was (not sure if it still exists) even a coffee shop in Koenji that served 2 1/2 year old coffee in a wine glass (Cafe French)
There are several coffee flavored food items around too including ice cream at Baskin Robbins, coffee jelly sold in supermarkets and convenience stores, coffee flavored cakes, and more.
