You can get to Northampton from London on the train in about 1 hour or to Milton Keynes in around 40 minutes and it's about 30 minutes from there. But it's not something you could do in a day really.
I really want to go to Monza or Spa. I know people who have and it's a damn site cheaper for a ticket to either than it is for Silverstone. Could also drive to Spa from here.
Spa is awesome and set in the most beautiful countryside
Went there with G Jnr to watch the 24 hour race last July.
Weather can be iffy sometimes