A really cracking day out would begin at St Paul's Cathedral. A word of warning; unless you want to attend a service, don't go on a Sunday, because you won't be able to wander around.

The Tower of London and Tower Bridge are just around the corner and we love to park up and visit Dickens Inn in St Katherine's Dock too. The historic building dates back to 1799 and was originally a spice warehouse.
Another favourite spot in this area is Dennis Sever's house in Spitalfields. The minute you're through the door, you feel as though you've been transported back to the 18th century. While you're in the area, you must visit 19 Princelet Street (now the Museum of Immigration and Diversity). It's one of London's finest examples of Hugenot architecture. Nearby you'll find the lovely Patisserie Valerie. Their custard tarts are the best for miles.
Other Central London historic haunts we recommend include the Handel House Museum in Brook Street, and Leighton House Museum on the edge of gorgeous Holland Park.

For an interesting day trip, head to Charles Darwin's home, Down House. You can even have a pint in the local pub that Darwin used to go to. It's called The Queen's Head, and it's in Downe village.
Another great out of town trip is Hampton Court Palace – not just because it's such a wonderful place, but also because the boat ride along the Thames is a dream.