Near Roppongi Hills there's a sushi place where you can pay a fix amount and eat as much as you want (should do also shabu shabu).
If you go to Jiyugaoka (from Shibuya, the line to go to Yokohama... just 10 minutes), there are a lot of good places to eat (ramen, etc. )
Ok, I'll check around if I manage to find some cards...
PS If you like Macha ice cream... for sure the best part is in Shinjuku in the underground passages. There's a small tea shop near the only place to donate blood. It's really , really good.
Ah, and also to the Meiji Jingu (Chiyoda line - Meiji Jingu station / Harajuku - JR Yamanote line), remembering to check also the side garden (the one you need to pay to go inside).
From there is walking distance to Shibuya, too, with the bonus of passing a lot of nice shops.
Ah, right... from Harajuku station, going down to Omotesando (so Shibuya direction), at the first big crossroad if you turn right you go to Shibuya. If you turn left, around 20/30 meters there's a chinese restaurant that should be quite good (always a lot of queue), specialized in desserts.