I'm a bit surprised the basic room at Strings is 35,000y, although I guess there are certain peak periods. Nonetheless, I'd recommend it over IC Tokyo Bay for your purpose. It's way easier to get to Keikyu from Strings than it is to get to the monorail from IC. Plus, you say you're looking to enjoy shopping and dining... there's not a whole lot around IC Tokyo Bay although I grant you that it will be convenient to get to Odaiba from there. If you stay at Strings, there's way more in the vicinity and you'll have better access to dining/shopping hotspots like Shibuya.

Also, if you're looking for luxury + view + access to shop/dine + value, then you may want to expand your horizon beyond Shinagawa and Hamamatsucho area. Staying in Shibuya will only add 15-20min on top of the Shinagawa-HND travel time.