Could look at Greenwich, there is the Mercure, and I think the other one is an Ibis.
After the show use the Emirates airway to get across the river to North Greenwich, then bus it to Greenwich itself where you have the Maritime Museum, Park, Cutty Sark and a load of pubs and restaurants for the evening.
Sunday, up, walk in the park, down to the river past the Cutty Sark to jump on a Thames Clipper ferry to the Tate.
I am a big fan of using your transport to see the sights when in London, rather than flicking between places on the tube and missing 90% of what there is to see.
Emirates Airway trip one way is about £4 on an oyster and you get a decent view of the Wharf, especially if it is dark, then the Thames Clipper again is about £4 and runs you up the river past loads of sights. Better views than the tube.
Edit: It’s the Emirates Airline, not Emirates Airway