Eating in in Shiodome area?
Stayed a couple of times at the Conrad but haven't been able to find that many good places around there. Wind up walking over to Ginza most of the time. It's pretty close and about a 15 mins walk. In the Caretta building, I did try the oden place last time and it was OK. Maybe it is because i am more used to the area but I always find the grand hyatt to have a better selection of restaurants nearby.
En, at the top of Shiodome City Center, is sort of an upscale izakaya with great food and a good sake selection (and English menus).
Yappari Tako (in the same building) is a wonderful octopus specialty restaurant, with nice tender octopus sashimi, interesting takoyaki, deep-fried octopus with garlic and much more; they also have some horsemeat specialties as I recall. And a good sake/shochu list. The manager used to work in the US and speaks English.
The Conrad Hotel in Shiodome has a nice Japanese restaurant that overlooks Hamarikyu garden and Tokyo Bay. The bento box lunch is exquisite with a variety of dishes gorgeously displayed.
China Blue, their Chinese restaurant also looks nice.
And, if you like teppanyaki, the Japanese has a teppanyaki counter with spectacular views.
At the very least, go up and have a drink in the bar. There is no cover charge before 8 p.m. otherwise add 1500 yen to your bill.
In the basement level of the Shiodome Caretta building (the one that houses the Shiki Theater) there's a branch of curry udon restaurant Konaya. The idea of curry udon never really appealed to me, but when I tried it here, I was blown away. Their deeply complex broth is fantastic and coats each strand of udon in rich flavor. It's the most badass bowl of noodle soup you'll ever have. I usually get the ebi ten curry udon in the picture at the link.
Across the walkway from Konaya there's what I guess you could call a wagashi parlor, that specializes in tea desserts. There always seems to be quite a line to get in, so I've never gone, but they have a little gift shop outside the entrance that sells a very good matcha soft cream.
If the weather precludes having a hot bowl of soup, there are several restaurants there that certainly look like they'd be worth giving at try.