I still don't really know what tastes I'm suggesting for, so I'm going to throw out completely random suggestions. As said, it would help to know what interests her.
daytrip to Bristol to see Charioteer sites daytip to Oxford or Cambridge (which involve a whole other list of "what to see") daytrip to Paris by Eurostar (or Lille, or Brussels) backstage tour at Royal Opera House whatever exhibitions are on at Somerset House exhibitions at the British Library Stanfords, very large travel store Thames path walk (could be multi-day if you continue outside London) hipster London - Spitalfields, Hackney etc Greenwich Park by DLR or river cruise Camden Market
And I would recommend trying to see some villages/small towns as well... completely different than London but easily reachable in a day. Fordwich the tiny place where lilliburlero and I stayed recently, is like an hour and ten minutes from St Pancras station.
no subject
daytrip to Bristol to see Charioteer sites
daytip to Oxford or Cambridge (which involve a whole other list of "what to see")
daytrip to Paris by Eurostar (or Lille, or Brussels)
backstage tour at Royal Opera House
whatever exhibitions are on at Somerset House
exhibitions at the British Library
Stanfords, very large travel store
Thames path walk (could be multi-day if you continue outside London)
hipster London - Spitalfields, Hackney etc
Greenwich Park by DLR or river cruise
Camden Market
And I would recommend trying to see some villages/small towns as well... completely different than London but easily reachable in a day. Fordwich the tiny place where