If you are a fan of Call The Midwife you can train out to the Historic Chatham Dockyards and tour where it and other shows have filmed. http://thedockyard.co.uk/whats-on/call-the-midwife-location-tours/
30-40 minute train ride from St Pancras. Pleasant 1/2 day sojourn.
You might also check out Richmond Park area and Twickenham. One year near Christmas was resting my feet at the Royal Academy of Arts and I overheard some one mention the artists collective open house on Eel Pie Island. How can one not go to a place with such an intriguing name?
Google and discover its famous residents over the years. I trained to Twickenham and wandered. Then found the bridge to the island but not before stumbling upon the intriguing York House gardens as well as watching the early morning rowing club enjoy an outing along the River. Had a pleasant lunch at the White Swan pub. Research Twickenham and Richmond Upon the Thames.
If you are willing to go farther and spend a night or two I love Lyme Regis. Stayed at a fantastic AirBnB and meandered along the Cobb and beaches keeping an eye out for fossils. I did have a car rental so didn’t train there but know you can train from Waterloo to Aximinster then take a bus to Lyme Regis.
In London use the tube and explore Hampstead and then stroll through the Heath into Highgate to visit the famous cemetary. From there tube to Kentish Town to lunch at Wahaca above the tube station or the Oxford Taver Pub on Kentish Town Rd OR walk from the tube station along Kentish Town road over the Camden Lock Market and find a food stall for your nosh.
Lastly you can always walk along the Thames path from Tower Bridge to Rotherhite and then to the Surry Quays neighborhood. Trust me no tourists to avoid.
If you have an interest check out the Sands Film Studio...http://knowledgeoflondon.com/sandsfilmstudios.html
All of these areas will provide freedom from hordes of tourists ( well Camden Lock market won’t but you have the adjacent canal to walk and explore. )
Enjoy.