There are some parts of Brixton where unwary strangers should not venture at night. (Before someone accuses me of labelling all of the citizens of Brixton in a negative way, I'll hasten to point out that there are lots of wonderful people, of all races andall ages, in Brixton. Depite that, I still wouldn't recommend that people who don't know the neighbourhood spend much too time in Brixton at night).
The nearest car park is the multi-storey one on Pope's Road. See here:
http://www.brixton-academy.co.uk/travel.php
Brixton tube station is within reasonable walking distance of both the car park and the venue. There are trains every few minutes and you can be in central London in about 20 minutes. For the best range of eating places, I'd suggest Covent Garden. (Take the Victoria Line for 5 stops to Green Park. Transfer to an eastbound Piccadilly Line for 3 stops to Covent Garden. If you'd prefer to take Lonnie's advice and go to Chinatown, just get off one stop earlier at Leicester Square ).
My favourite restaurant in Covent Garden (excluding the really expensive ones) is Bistro 1 on Southampton Street. To get there from Covent Garden tube station, turn right out of the station and walk straight on until you reach Covent Garden Piazza (with the former market building straight ahead of you). Find your way to the other side of the market building and you'll find Southampton Street. Bistro 1 is on the right.
If you really don't know London at all (and the weather's good) you might just enjoy wandering around central London. Covent Garden and Leicester Square are in 'Theatreland'. (There are plenty of cinemas in the area as well). They're close to Trafalgar Square and the Thames. On a pleasant evening, London is a great place to explore.
For a guide to what's on at London cinemas, pick up a copy of 'Time