For lunch, the Dulwich Picture Gallery Cafe is really nice. And the museum is lovely.
We've been told that Green & Blue on Lordship Lane is very good, but we haven't had a chance to try it yet.
El Querce is further afield, but makes wonderful simple pasta and very imaginative gelato.
There are a few places in East Dulwich to try. You could always try posting on The East Dulwich Forum, or doing a search on there for restaurants in the business section.
What kind of food are you thinking of?
Some suggestionst:-Franklins in Lordship Lane SE22, Le Querce (home made Italian) in Honor Oak Park/Brockley SE4 or The Palmerston on Lordship Lane, SE22. There is also Ganapati in the Peckham Rye part of SE15 which has wonderful South Indian food. All these places have free parking mostly with the exception of Ganapati during the weekdays and on Saturday.
Or you could go up to Brixton Village (whole different separate thread on that) and if it is on Sunday or after 630 you could park for free.