After arriving at Heathrow, take the bus directly to Rove Hotel Paddington to drop off luggage. This will help lighten your day as you explore nearby areas.
Visit the Buckingham Palace area for photographs outside the palace. The State Rooms tour is pricey, but the exterior and Victoria Memorial are beautiful and free to enjoy.
Enjoy the quiet atmosphere of the nearby London Library and appreciate historic collections (check access rules as some may require membership, mainly for reading rooms). Use as a peaceful spot if allowed to visit.
Take bus to the Tate Modern for impressive modern art with free admission, open from 10am but arriving early allows you to enjoy nearby Southbank walk.