I'd probably take the bus to ANA (if you don't have to wait too long for the departure). ANA is the first stop, traffic should not be too bad, and it's a quick easy 5 minutes cab from ANA to the Ritz.

As others have suggested NEX to Shibuya is a good option also.

NEX to taxi (Marunouchi North Exit) is easy if you know what you're doing but can be confusing.

Another option if you don't have much luggage is NEX to Tokyo, transfer to Marunouchi subway line (very easy), two stops toward Shinjuku, transfer at Kasumigaseki to Hibiya line for Nakmeguro (extremely easy transfer.....50 meters from the front of the Marunouchi line platform), two stops and get off at the rear of the platform at Roppongi, go out exit 4a. From there a 250 meter walk to the hotel. (This is the cheapest and quickest option).