Not knowing what you like, it's difficult to say but..
The London Jazz festival is on, and this is free: www.londonjazzfestival.org.uk/event/1449/ljf-sessions-ray-s-jazz-free
If you're dressed relatively well, you can go for a cocktail in the Savoy, which is amazing and makes you feel proper fancy. Or you can have a drink in the restaurant at the top of the National Portrait Gallery, which is open until about 10 and gives you an amazing view from Trafalgar Square down to Parliament.
Go and watch a debate in the House of Commons: www.parliament.uk/visiting/visiting-and-tours/ukvisitors/debates/
It's free, and despite what it says on the website, you don't have to queue unless you're trying to see PM's Questions.
Or have a Google and see what guided walks are on.
For dinner, there's a Leon on the strand, which is a chain, but it's good value in an expensive area.
Have a drink in Gordon's wine bar, just off the Strand, near Embankment station, because it's so cosy and feels like an older version of London.
Hmm my suggestions do seem to involve a lot of drinking, but in nice places rather than standard pubs, so I hope that's okay.