Unfortunately there aren't any particularly convenient National Trust properties nearby. Here's the results of a search based upon the postcode for Marylebone Station:
http://www.nationaltrust.org.uk/575-wandsworth-road/visitor-information/
All of central London can be accessed fairly quickly by Tube though, so you won't be short of things to do!
I'd suggest heading to South Kensington, where you'll find the V&A:
http://www.vam.ac.uk/
From Marylebone take a Bakerloo Line train to Paddington (2 stops) and then a Circle Line train to South Kensington (5 stops) OR take a Bakerloo Line train to Piccadilly Circus (4 stops) and then a Piccadilly Line train to South Kensington (4 stops).
In the unlikely event of you not enjoying the V&A you can simply cross over the road to the Natural History Museum or to the Science Museum. (They're all free, so it costs nothing to poke your nose inside to see if 'it's your type of thing'. Don't try to do them all though, as they each need several hours exploration to get the best from them!).
From South Kensington, then take a Piccadilly Line train to Covent Garden (6 stops), where you can enjoy the general 'buzz', watch the free street entertainment (usually including some excellent opera singers) and then get lunch at Bistro 1 on Southampton Street. (It's got lots of fans here on AB, with a good-quality 2-course lunch costing just £9.90). Menu:
http://bistro1.co.uk/menus/bistro1-restaurant-lunch-menu.pdf
It's then only a 5-minute walk to Trafalgar Square, where you can visit the National Gallery (another freebie):
http://www.nationalgallery.org.uk/
and/or the frequently-overlooked National Portrait gallery (which is behind the National Gallery):
http://www.npg.org.uk/
From there you can easily walk to one of the world's best (and quirkiest) wine bars, Gordon's, (which is down the side of Charing Cross station, near Embankment Station) where you can treat yourself to a bottle of something really nice:
http://gordonswinebar.com/#!/gallery
From Embankment Station it's just 6 stops on the Bakerloo Line for you to get back to Marylebone. (Your niece can get back to Stratford by taking the Circle or District Line to Monument and using the escalator link to Bank, from where she can get the Central Line).