Hi Alice,
Here are a few of my favorite stationery stores in Tokyo with a huge focus being on Japanese handmade washi paper because that is what I was stocking up on at the time. You will want to check the internet before you go for the latest address (a couple of these shops had moved from their original locations the last time I went back several years ago), public transit directions, and hours. Many shops are closed on at least one weekday. Some of the larger train station also have stationery stores in them and I've found some nice items unexpectedly this way.
Ito-ya Ginza - literally my favorite stationery store in the world, complete stationery overload, multiple floors, allot at least a couple of hours to look at everything. There's an entire floor of Japanese washi paper, and another floor of fountain pens. You might find calligraphy items on the fountain pen floor (my interest in calligraphy hadn't started yet when I last visited). Check out this article about the new Itoya after it went through a recent renovation:
http://mcha-jp.com/14032Haibara: beautiful washi paper and stationery,
http://www.haibara.co.jp/en/Kurodaya: washi paper, stationery items and gifts, not sure if they have a website (I just quickly Googled), the last address I have for them is 111-0032 1-2-5 Asakusa, close to the big temple
Ozu-washi: washi paper store and museum, last time I was there they also had washi paper making demonstrations,
http://www.ozuwashi.net/englishBos and Needle: beautiful boxes of all sizes covered in washi paper, boxandneedle.com
Sekaido Shinjuku: I haven't been here but Maybelle Imasa-Stukuls likes this store for calligraphy items,
http://www.timeout.com/tokyo/shopping/sekaido-shinjukuAs far as where to eat, I think it's difficult to go wrong. There are many great ramen shops, to the basement floors of department stores covered in beautiful a la carte food items and bento boxes, to Michelin starred restaurants. If you like sushi, the Tsukiji fish market experience is hard to beat and you can have sushi for breakfast as long as you're still jet-lagged and up anyway.
Have a wonderful and fun trip. I think if you visit all of these stores, or even just a few, you will leave significantly poorer.