The Hilton Kensington is quite well situated for Hyde Park and the park is good for training runs. I used to run there when I was staying in London and training for the NY marathon last year. What's good about it is that you can vary the routes and circuits depending on how far you want to run or how you feel, and there are things to look at (I sometimes - well, often - needed distracted from how tired I felt!) on the way.

The other place I often ran (which isn't so handy for where you're staying) was in the Regents Park and Primrose Hill area. Again good for varying routes.

I don't like dodging traffic so these were my best bets. You can run alongside the Thames but I think the parks are better as you don't just head out in a straight route then back.