If you like live theater, experience a play at St. Martins Theatre. Check online for times and prices.
You'll have no end of sightseeing choices when visiting London City Centre. St. Martins Theatre is a great place to start here, but there are plenty of other worthy sights to appreciate. Buckingham Palace, Big Ben, and Trafalgar Square are near the arts and culture attraction and and will cap off your day nicely.