I haven't stayed at any of the three (I live in London) but based on location I would go with The Connaught or Claridge's. Knightsbridge is a snore - I much prefer Mayfair. I've had a drink at The Connaught's bar and it seems like a really lovely hotel - great decor. Claridge's seems a bit more traditional. Both are within a few minutes walk of each other - Claridge's a bit more convenient to Bond St Tube and Oxford St (if you must...). Hyde Park isn't far from either (closer to The Connaught). Shopping is probably a bit better from The Connaught - there is a Balenciaga boutique basically next door - though Claridge's is right near Brown's and a tad closer to New Bond St.