London is going to be expensive for the incidentals especially - food and drink etc. My advice on this is that you can get it a little cheaper if you opt to take it away - like a coffee and a muffin etc. It’s getting warmer now, so she should be able to take this away and sit by the river or in a park and not get too cold.
If she’s around on a Friday/Sat, my absolute favourite thing about London is called Borough Market - huge outdoor farmers’ market under the train tracks on Southbank selling all sorts of food and drink, both cooked and fresh, which is amazing just to wander around, but good for a cheap lunch. This is walking distance from the Golden Hind (replica of Drake’s Elizabethan era sailing ship), and Tate Modern (also free), the new modern art gallery built inside an old power station. The Turbine Hall hall itself is worth a look. Across the river is St Paul’s, also good for views of Tower Bridge (not called London Bridge).
As mentioned, most of the museums are free, and so are the big department stores in Kensington - Harvey Nichols and Harrods. I also like walking around St James Park and up towards Picadilly - past all the expensive shops on New Bond Street, so pricy that you don’t even get the feeling you wish you had a little more money to spend - just astronomical.
Avoid Oxford Street and Picadilly Circus (too crowded and full of tourists), wander instead through Soho and Covent Garden, through Old Brompton Road (kind of known for being the ‘gay’ street, but facinating and less sterile than parts of London), and around Monmouth Street and Seven Dials. All of these can be found easily on maps online, like Google Local.
If she’s around on a Sat, Portobello Rd market is on in Notting Hill (touristy, yes, but still free and busy), and on Sunday and I think a few other days Spitalfields Market near Liverpool Street Station is also meant to be great - haven’t got there yet. Sunday also for Camden Market - facinating stalls and also a chance of seeing ‘real’ punks - albeit that they’re all around 15…
For travel, think about getting an Oyster Card if she will be doing a lot - this caps the travel on tubes or buses at the max of a daily pass. But walking is free and the best way to see the sites. If you need public transport take the bus - it’s around £1.50 per ride, get on, go upstairs and see the sites as you drive past - face it, just about anywhere you go is going to show you something different and famous.
Unless it’s really important, don’t bother spending the cash on tours, Westminster Abbey (£10), Tower of London, etc. Haven’t been up the London Eye (it’s around £14), but have heard on a clear day it’s worth the money.