I stayed at the old Akasaka Prince back in the day, and for old time's sake went to both bars at the new Prince Gallery in October. They were a little on the pricey side, but nothing too ridiculous by Tokyo standards. I'd imagine the rooms are probably beyond my budget, though.
Not sure if you're familiar with the general area, but Akasaka-Mitsuke station is on both the Ginza and Marunouchi subway lines, which makes it very handy to Ginza, Shibuya, Shinjuku, Tokyo, Ueno, and most places I can think of off the top of my head. The hotel's not all that far a walk from Roppongi, either.