Hindhead – they’ve shut the old A3 now the new tunnel is open. Park up at the National Trust cafe car park, ride around the Devil’s Punchbowl and back to the cafe for lunch. The trails are good and the views, especially from the top of Gibbet Hill, are brilliant.
If you give me an idea of the distance and hilliness you and your other half would like to ride, I’ll suggest a route.
Also, any of the Surrey Hills from Westcott, Holmbury or Peaslake are excellent, too. Or you could head further down the A3 to the Queen Elizabeth Country Park just south of Petersfield.
Being in London, you’re at the hub of a bunch of railway lines that lead to various points along the South Downs Way, so why not do it in sections? Get the train to Winchester and ride to Petersfield then do Petersfield to Amberley, Amberley to Brighton and Brighton to Eastbourne on other weekends.