Just FYI, it's absolutely bloody freezing in London at the moment. Like the five minute walk home from work is unbearably windy and cold.
I would avoid anything that involved walking and you couldn't pay me to get on top of a tour bus *brrrrrr*
Tour busses are great if you want to see the whole city but they are freaking expensive, £25 a person o_O
You can avoid the tube and get regular busses to get around, depends if you want to see as much as possible or just do one thing.
Non touristy, that depends on what day you're coming in? Different things on different parts of the week
Vintage clothes shopping trawl down Brick Lane, Street food market? Best pancakes in London? etc.
I would avoid Covent Garden itself like the plague, and I live there!
I don't really see the *point* of it, there's nothing there aside from the moomin shop and Laudree that isn't somewhere else (oh and Meat Market), too many tourists and I want to punch all street performers in the face.
There's some nice boutiques and places around 7 dials if you are in the covent garden area.