It�s a difficult one as it comes down to a matter of personal taste. Are you happy enough to sit listening and watching an orchestra play, or would you prefer something more, maybe some singing (opera etc) or dancing (ballet etc) as well?
The major venues in London are:
Royal Opera House
Southbank Centre (Royal Festival Hall, Queen Elizabeth Hall, Purcell Room)
Wigmore Hall
St John's Smith Square
Barbican Centre
Royal Albert Hall
London Coliseum (ENO)
RPO website has national listings as well.
You could look at the venue listings on their websites to see what might appeal to you. If you are not really into classical music as such, you might prefer a mixed repertoire by several composers. Opera and ballet tend to feature the better known/popular pieces. Alternatively hear pieces from film and TV such as:
http://www.rpo.co.uk/c_t_rpo_season_detail.asp ?ConcertID=966
As Naomi has said, if you want a bit of light hearted fun, variation and intro to popular classical pieces, try the annual Classical Spectacular at the Royal Albert Hall (November) its good family fun and not too heavy.