Hakkasan has a very cool vibe and a Michelin star, no less. It is not quite a jaw dropper, though, and is on one of the dingiest streets in London!
Sketch is probably the coolest from a modern design point of view - the pod toilets are like nothing you will have seen before (or will see again!).
The finest dining room in London is The Ritz. It is also laughably expensive. However, Sunday lunch is a relative bargain and you may want to try that. Jacket and tie for men. The bar is also very impressive.
For something a bit way out, take a look at Wapping Food which is a restaurant built into an old power station, with most of the equipment still in situ.
Galvin At Windows, on the top floor of the Hilton on Park Lane, has astounding views and reportedly good food - I am going later this week so can give a fuller view next week if required.
If you're staying in Soho, The Soho Hotel is still a cool place to hang out although you can enjoy it just as much by going for a drink than a meal. (In fact, I can't think of another hotel in Soho - based on definition of Soho - so I assume you are staying here?! It is a super place and very trendy.)
squaremeal.co.uk is a good place for restaurant reviews - this is aimed at a City clientele so you can normally rely on what they say.