Hi, I can't talk direction about the area you will be in, but its about 5 mins walk to Kennington Tube (Underground/Metro) station and you can get to London Bridge (Borough Market, London Dungeons) or go to Leicester Square and walk up to Oxford Street (shopping) or go to Covent Garden (Punch and Judy pub, street theatre).
Practically the trains run so frequently up to nearly midnight (may be up to 12.30am - check carefully) so any part of central London is there for you to choose. As for pubs ... well depends what you are looking for. There are great old style pubs, as well as more trendy bars, music places and comedy evenings. Check out beerintheevening.com.
Cheers, Colin. over 6 years ago