Gosh that's a wide question, London's a big place with a lot of choice! Are you coming in on the train and if so to which station, it might be nice to have lunch somewhere in the vicinity of the station before heading on to your activity?
In terms of an activity, what kind of thing were you thinking of - sight-seeing, cultural, sporty, animal based, niche interest such as Harry Potter or Haunted London or geeky stuff? Personally I would love to do lunch in Chintatown, go to a West End matinee and perhaps spend some time browsing second hand books on the Charing Cross road but that might not be at all up your DD's street 
. Have you done the classic London sight-seeing stuff, a river cruise on the Thames, the London eye, Tower of London, Buckingham palace, the museums? If not it might be nice to fit one of those in. Or if you were thinking something more active lots of activity based pubs have popped up in London recently where you can do an activity and get some food and have drinks which teens/younger adult seem to love e.g. Flight Club for darts, All Star Lanes for bowling, there are ones for crazy golf, axe throwing, pretty much anything if you google. A walking tour based on a specific interest might be nice too, there are loads of different ones, again google or Viator is your friend. For shopping obviously Oxford Street/Bond Street are the famous ones, personally I find them underwhelming as the same high street stores you'd find in any city centre (just big!) and always very busy (then again I am not a shopper by inclination!) but if she's never done Selfridges/Harrods/Fortnum and Mason it's worth seeing once. If you're more intense shoppers then the Westfield malls are nice (air conditioned!) and have lots of food options too. Teens also seem to enjoy Camden Market particularly if they are a big alternative-leaning, and there's a new food marker just up the road where you could get a street food lunch too. Or if you want full on hipster and vintage type stores Shoreditch/Hackney/Hoxton is where it's at (I think, probably by the time the likes of me get to here about it the true cool kids have moved on!).
Re steak, how much were you wanting to spend? Hawksmoor is the classic for steaks but £££. A more mid range option would be Blacklock who have either a Soho or Shoreditch branch. Or the steak lovers I know rave about Le Relais De Venise Entrecote (sometimes known as just Entrecote) which is a French small chain with a set menu - salad, steak frites and sauce only served Parisien style.