If you want things in the immediate vicinity then the delights of Shinagawa won't be particularly obvious. There is an awful lot around a 30 minute walk radius from this hotel, but they don't have the razzamatazz attraction which other areas can spoon feed you.
The attraction for most tourists is the transport connections - access to the Yamanote line is fast and painless, and in less time that it can take someone to alight at Roppongi station and get to the surface exit you could already be at Shibuya or Tokyo having bought your ticket in Shinagawa. You only depend on your local area for amusement between midnight and 5am when you're at the Strings as it's so easy to go elsewhere.

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ANA IC - wasn't a huge fan of the neighbourhood, but with Roppongi Hills and Tokyo Midtown nearby I won't argue that there is lots to do. Getting most places elsewhere with transport will take at least 50% longer than from the Strings.
If you are prepared to walk a little then there is a neighbourhood I really enjoy nearby which is Azabu Juban. Takes just under 30 minutes.

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Shinjuku - this is 'Lost In Translation' Tokyo. The quintessential area for many. Easy to spend a few days here and never see any other part of Tokyo. Easy transport to other parts, you can walk to Harajuku.

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Shibuya - Kind of like a compact Shinjuku, but with a younger vibe. Some hip neighbourhoods within walking distance. So even though I'm not someone to hang out in Shibuya, it is a convenient transport nexus and neighbourhoods like Daikanyama, Omotesandoo and Harajuku within 30 minutes mean that this might be the best option if you want to walk to interesting nearby areas.