The Okura is not a cheap hotel - but if you can get a corporate/group rate it helps! The staff speaks good English & the service is great. They also have a good sized gym & proper lap sized swimming pools (indoor & outdoor)- I believe you can use the outdoor pool for a fee in summer time even if you aren't staying at the hotel.
The down side from my point of view is the location - it is just too far from anywhere to walk easily (about 25 minutes to Roppongi)-& the nearest Subway (Toranomon)is 10-15 minutes away (don't believe thenm when they say 5 minutes!)This means you have to take taxis everywhere or you're limited to eating in the hotel every night (which you don't want to do because it's expensive).
However, the recently opened 'Starbucks' in the Shiroyama building just behind the hotel now gives a new alternative for breakfast/snacks & the constantly developing food/shopping court in Ark Hills (10 minute walk) means that eating prospects are improving in the area.