I spent a year in Tokyo in 2005 and am heading back for 24 hours in February. Needless to say I want to make the most of my time especially when it comes to food. I am staying at the Park Hyatt in Shinjuku (finally!) and don't want to travel too far from the hotel. Which of these options would you recommend or would you have any others?

Kakiden
Hotel de Mikuni
How is Kybei in Keio Plaza. I went to the one in the New Otani (or was it Okura) Hotel and thought it was very good.

One of my favourite restaurants in Japan is Daigo (shojin ryori). I don't believe that's anywhere near Shinjuku though. Any alternatives?

Any other options?

Many thanks!