London has a lot of sights to "see" and I would agree that walking along the south bank form Tower Bridge to the Houses of Parliament offers a lot of good value and is the obvious thing. From HoP you can continue along Whitehall to Trafalgar Square and then go left up the Mall to Buckingham Palace, taking look at the Pelicans and/or head on into Soho. Give Leicester Square itself a wide berth but China town & north from there has value.
But for my money
do not bother with
1) Borough Market, at least not on a Saturday. Too many people, too expensive. Not real. Brixton market is better for my money these days, or maybe Maltby St but that is not that big a London experience.
2) Covent Garden - it is pretty much a high street shopping experience in a nice-ish place but with tedious street performers
Recommending things to do any more depends on taste - if you want to go shopping then there is a spectrum of experiences, from Oxford St & Selfridges, to Knightsbridge with Harrods & Harvey Nicks or an indy experience around Camden lock. Personally I'd sooner slit my wrists than go to Hamleys.
I'd only suggest the Emirates cable car if you have kids - beware it goes nowhere unless you are on the way to something at the Excel centre. If you want a view of London, apparently you can go up the Shard or Heron Tower in the city to bars that have great views. I'm not saying the glass of vino will be that cheap but various people have commended these strategies.
But my top tip if you want to see something unique to London and indeed something close to the part where your hotel is, take a walk north to Brick Lane. Don't go there for the cliche of curry houses but for a full diversity of world food, edgy fashion and a cultural mix that is pretty unique and a great part of East London. Go a little further north on a Sunday morning and see
Columbia Road flower market. You'll do this having walked through the city past the Gherkin, Heron Tower etc. as well. Note, Spittalfields market is a private equity enterprise. Trying to pick up cash from the city and wannabe east london venturers it's purpose is to filter out people with more money than sense from getting to sensory extravaganza of Brick Lane.