Well, if you havent been already, you should definitely go to the Mori Museum, in Rippongi.
It is on the 53 and 54th floors of a modern skyscraper, with changing shows, so you never know what will be there.
Then, if you have the time, I highly recommend taking the train out to see some of this guy's work- he is a crazy Japanese Art Noveau architect who changed his name to Vonjour Caux, and his stuff is unbelievable. I know some really good japanese blacksmiths who worked with him quite a bit to make the ironwork for some of his projects, which are mostly apartment buildings, and every detail is amazing.
Then, there is this sculpture park, http://www.hakone-oam.or.jp/eng/
which is a couple of hours by train.
The big museums, up in Ueno Park, are all pretty interesting too- there are something like 6 of them there, along with the zoo.
I really like a couple of the specialised department stores- Tokyu Hand, which is kind of a crafts/tool store, over in the Shinjuku train station complex, and is pretty cool.
And, depending on what kind of art you do, you might enjoy Yuzawaya- this is a chain of GIANT craft supply stores- the one I like best is out in Kichijoji neighborhood, is something like 7 stories tall, with every kind of craft and art supply, usually very nice quality japanese stuff, too- beautifully made crochet hooks, or little brass rulers, high quality materials of all sorts, in store classes in some things.
Kichijoji in general is kind of interesting- its a quiet, suburban Tokyo neighborhood, which means about as busy as the biggest US cities- with a nice park, with a lake in it, about a ten minute walk from the station, interesting hipster stores, and just normal japanese life. Its a few stops past Shinjuku to the west, where tourists never go.
I had a great time walking thru the kitchen supply neighborhood, Kappabashi Dori, which is near the Asakusa subway stop, which has whole stores that sell nothing but perfect plastic food, and the most amazing knife stores. Need 100,000 chopsticks- buy a bundle.