Lazyweb: London

I'm planning to take April to London for a day or two on October, and I'd like some help: I need a child-friendly hotel somewhere in central London.

There are precisely ten bajillion hotels in London, and I'm struggling to find something that fits the bill. It doesn't need to provide anything in particular, just to be suitable for a three-year-old and her dad and the price needs to be in the 'sane' range (i.e. I'm not on anyone's expense account but my own), but I'm prepared for what London costs. Bonus points for being very near an Underground station and perhaps extra bonus points for being near Paddington station, where we'll arrive from Heathrow. We're basically visiting the Tower, Buckingham Palace and the London Eye, if that helps to narrow it down.

Any personal experiences or recommendations would be great. Thanks!