Local spots near Grand Hyatt in Roppongi, Tokyo
jkrell, when you mentioned "local spots", are you only referring to Japanese eateries?
If you happen to like Indian food, there's Samrat which is 5-10 minutes' walk from Grand Hyatt. The reason I mentioned it is because, a couple of years back, and friend & I decided, for a lark, to dine on ONLY Indian food every night for the whole 2 weeks we were in Tokyo (that's because we travelled to Japan so often and had eaten in so many Japanese places, we wanted to do "something different" for a change). We subsequently went all over Tokyo in search of a different Indian dining spot each night. We found Samrat pretty good, so much so that we went back there a couple of times.
As for Japanese eateries, there are certainly no shortage of good ones in the Roppongi Hills vicinity but I think Tokyo-based Chowhounds would be in a much better position to advise you on the latest hotspots.
Roppongi, Tokyo , JP