Obviously, London is a huge city ( current population about 8.8 million) and many weeks could be spent exploring it. On most visits I end up walking in excess of 12 miles whilst exploring.
I live close enough to visit regularly, especially in the summer. Often cheap day return tickets are available for the train ( The better option if you fancy a few drinks whilst exploring the city.) Sometimes I drive, park on the outskirts and tube in to my chosen destination for that day.
There are so many photo opportunities in London, people, animals, buildings, transport, flowers and plants, the river and objects. If I am on my own I tend to wander aimlessly and try to explore streets I have not been along before (I lived there for 12 years). However, for example, on one of my trips I found a hidden pub in the heart of Covent Garden that I did not know existed.
Particular walks we have done are,
South Bank and City: We start at Westminster and walk along the south Bank to the Tate Modern. Then over the Millennium Bridge towards St Paul’s then wander the Bank area streets. Of course you can hop on and off the tube or buses to move to another location.
Canary Wharf: A must if you like architecture. You wander around looking up, try not to, there is plenty to see a ground level to. You do feel like you are in a truly futuristic city. The streets are clean and vibrant except for the weekends, then it’s very quite. Pleasant in its own way though.
The Parks: Plenty to choose from and each has its own personality. Hyde Park can tend to be the least interesting but does have some merits. Walk from the end of Oxford Street through to South Kensington. St James Park will be much busier but after exploring it, look out for tame squirrels and birds looking for food, Head for the Downing Street area and explore the street.
Hampstead Heath: here you feel, a little, like you are in the countryside but it can get very busy which spoils it. However the views from the top of the hill are great. After this you can explore the surrounding streets of Hampstead and have a nice café lunch or dinner. The day we visited the Heath we had in fact been to Highgate Cemetery. It does cost £7.00 to enter but well worth the visit. It is really interesting (the only downside; you must take the guided tour). Brampton Cemetery is also worth a visit.
Borough: The area is dominated by the Shard (one of my favourite modern buildings, you must go to the top! Close to the Shard is Borough Market and its surrounding street.
Brick Lane: A clash of cultures and well worth visiting. In the late-19th Century thousands of Jews moved into Spitalfields in the Huguenots’s wake. Now its is mostly Bangladeshi and is known for its curry restaurants. But as you wander there are fabulous examples of street art etc.
Camden and Area: Camden Market is a place that you visit at least once but the surrounding areas are great to explore. You may even walk along the canal and end up in Regents Park. It certainly has changed since I used to visit in the early 70’s. In fact my very 1st visit to Camden was to see Godspell (1971) at the Roundhouse. Also in 1973 I went to see (Opening Week!) The Rocky Horror Show at the Royal Court Theatre Sloane Square. It was incredible especially for a young Northamptonian.