I took my partner to Tokyo for her first visit last year - around this time. I recommend the following :

Day trip to Enoshima & Kamakura, make sure you use the overhead monorail from Ofuna to Enoshima (http://kamakura-enoshima-monorail.jp/) and Enoden to Kamakura. Take in the Buddha if you have time. Great day out.

Afternoon in Shimo-Kitazawa, lots of quirkiness here and some nice little cafes.

Day in Yokohama. Go on the MV Hikawa Maru - Charlie Chaplin's favourite ship.

Shopping in Shinjuku (not my favourite day but it has to be done for those pressies to take home).

Day on Takao-San or Hakone. The latter gets you nearer to Fuji and you can get a funicular/cable car trip to Lake Ashi to get a good view. The former is also a great day out in the mountains.

Lots of museums in Tokyo so I won't bore you with a list... most of them are wort a go.

Eating good food in Tokyo is a breeze. If you're unsure just ask for an English menu (Eigo no menuu ga arimasu ka) or look puzzled. My partner was amazed at the range of good food and just how easy it was to get it, though it helps she was with a 30 year veteran of the place

Anyway - I think I got the balance of activities right because she loved the trip and wants to go again. You really can't go wrong in Tokyo even if you just "wing it" by roaming around. Get a suica card each for the trains/underground. Saves hassle.

Enjoy!