I love for example the prehistoric monsters in Crystal Palace Park. They are not much known but they are one of the city's treasures. You can't actually touch them but they give a wonderful near hallucinatory effect if you get them in the right light. I would also have a look at the Swedenborgian church in Waldegrave Road in Norwood. It was built out of concrete in 1883, which was not a habitual building material at that point. Someone put some pink pigment in the aggregate and the concrete did not stand up to the elements well. The whole thing now looks like the inside of a Crunchie bar, only pink.
There are countless places. My favourite house in the whole of London is on Church Road, Upper Norwood. I think it is owned by an ancient dentist. It was built in the 1880s and is very atypical Gothic. It looks like the Bates' Motel. Behind the Horniman Museum in Forest Hill there is an extraordinary group of roads which are very high up. You stand on the hill and you can see right over London.
I wouldn't eat in south-east London, the restaurants are pretty bad. I'd sooner have a packet of crisps in the car. I also wouldn't want to live there. I'd find it too preoccupying.
The series 'Further Abroad with Jonathan Meades' starts on Friday, 7 Jan on BBC2