[smithlane]

Rules is the oldest restaurant in London and serves typically British food so should appeal to the whole family. It's close to Covent Garden so very central and is nice for a special occasion. Failing that the Big Easy is just opposite and is a great Lobster and Steak BBQ restaurant that would definitely appeal to kids.
I agree the Shard is expensive for what it is but on a clear day the views are amazing but it gets ridiculously busy up there especially on a weekend.
Tower 42 is another option. It's been quite a few years since I've been up there but there is a Champagne bar on the 42nd level called Vertigo 42, lovely views from the other side of the river to the Shard. It's in the city not far from London Bridge