No worries — I hope you enjoy! I know you’re off tomorrow, but I asked my partner and they responded with this:
If they've got a few days I would recommend travelling out from the centre a bit e.g. to Greenwich (not lesser-known, but there's so much to see), to Hampstead (you've got the heath, the hill garden + pergola, and Kenwood has an excellent art collection and is free). In central London, Sir John Soane's museum is an absolute gem. Not sure how famous the Wallace Collection is, but always worth a visit, and apparently the Courtald's looking great after the recent makeover (still need to take a look for myself). It's many years since I went, but the Cabinet War Rooms (now unfortunately re-named the Churchill War Rooms) were good. As you know, for £5 it's worth seeing something at the Globe. Leadenhall market is getting known, but might yet be a bit off the tourist trail. Also, may not be to everyone's taste, but I do like the Barbican!
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If they've got a few days I would recommend travelling out from the centre a bit e.g. to Greenwich (not lesser-known, but there's so much to see), to Hampstead (you've got the heath, the hill garden + pergola, and Kenwood has an excellent art collection and is free). In central London, Sir John Soane's museum is an absolute gem. Not sure how famous the Wallace Collection is, but always worth a visit, and apparently the Courtald's looking great after the recent makeover (still need to take a look for myself). It's many years since I went, but the Cabinet War Rooms (now unfortunately re-named the Churchill War Rooms) were good. As you know, for £5 it's worth seeing something at the Globe. Leadenhall market is getting known, but might yet be a bit off the tourist trail. Also, may not be to everyone's taste, but I do like the Barbican!
Hope that’s helpful :-)