@PeachCriticthe arena isn’t in the Docklands, it’s in Stratford.
OP definitely no need to stay near the area. It’s simple to get to on public transport from anywhere more central in town. I’d stay as centrally as possible. It all depends on your budget as to the hotel of course. if I had £££ I’d choose the St Pancras! Alternatively the Premier Inn on St Martins Lane is well located for everything.
Assuming your train arrives at Kings X then anywhere from there down through Bloomsbury to the West End would be easy enough though.
Agree with others to try term time / mid week if do-able.
Show-wise it depends on what kind of thing you like. Theatre Monkey has good specific advice on best seats in the West End theatres. You could also go to the National to see something and explore the whole of the Southbank from Waterloo to London Bridge which has excellent places to eat and drink.
7-Dials and surrounding streets are nice to explore if you’re going to a traditional West End show around Shaftesbury Ave etc.
My personal favourite is mischief theatre the Play That Goes Wrong if you’ve not already seen it and feel like a belly laugh.
Also the area around Kings Cross / Granary Square is quite nice to explore if you end up with time in your hands before the train back.
other nice places to explore minus the theatre are the City of London / around St Paul’s, Leadenhall Market for lovely food, and river clipper (uber boat) to Greenwich and walk up to the viewing point at the Royal Observatory.