It's highly likely you'll be a tad fragile....! However, from where you're staying I'd suggest you potter gently along the South Bank - you can walk all along the river from your hotel.
There's always lots of things going on, a fab food market serving anything from crepes to paella to hog roast and Japanese and more.
Or you could wander into Town and up through Trafalgar Square, through to Leicester Square, Soho, Chinatown and Piccadilly/Regents Street etc. if weather is good, grab bits from M&S and head into St James's Or Green Parks for a picnic.
I'll have a think this week and let you know anymore thoughts next Saturday
If you don't want a huge lie in one Sunday, I'd definitely recommend heading to Columbia Road for the flower Market. The little shops and cafes there are gorgeous too. You're not too far from Brick Lane for proper bagels and then can wander to Spitalfields for shopping and mooching. My favourite Sunday morning pre-kids!
Don't know if it is your type of thing but there is a ballgown exhibition on at the V&A.
Hanging out in Primrose Hill on a (nice weather) Sunday is also lovely and chilled, wander round the park and nice shops, celeb (or maybe just paparazzi spot, get delicious brunch in one of the cafes. Easy to wander down to Camden market if you fancy a (major) change of scene.