There's a branch of Browns on Maddox Street (just the other side of Regent Street), their menu is a bit of everything and a decent choice for children.
Also a branch of Bella Pasta on Argyll Street, just across the road from the theatre.
If it's just snack type food you want (pizza, potato wedges, salads, etc) then believe it or not but Topshop is a good choice - they have a cafe on the lowest floor and the food is really good and reasonably cheap.
There's the slides at Tate Modern that children (and adults!) seem to love - they have height restrictions but i don't think it's very high for the level 2 slide.
The Science Museum is great for children as they have alot of interactive stuff there.
If the 6 year old is a girl, or even a boy into Kylie i guess, there's a Kylie exhibition on at the Victoria and Albert showing costumes all the way from Charlenes overalls to the gold hot pants and lots of pictures, etc. It's v popular though so you have to go online or call in to book a time.
Personally i'd leave the car and use the tube, especially if there's a few places you want to visit.