Definitely avoid Leicester Square for food, over inflated prices for mediocre meals.
Regents Park is amazing if you are around Bond Street area. If you walk through you can have a picnic and you maybe able to see the Giraffes in London zoo poking their head out amongst the trees!
If you are close to Kings Cross, Granary Square is lovely. Lots of water fountains, lovely little coffee shops and independent cafes. I would recommend Bodega Rita’s. You can get a takeaway sandwich and then sit by the water.
Bone Daddies in SoHo is amazing for Japanese ramen, it is a chain, but it’s fab. I would suggested getting the chicken Karage bun!!
You can do a Thames boat cruise, get on by Westminster and it’s takes you all the way down to Greenwich. I think it’s about £16, the tour guide is fab though and it’s really interesting. You can pay less and get off at Tower Hill. I wouldn’t eat round there though it’s very ££££
From Tower Hill you can slowly meander to Shoreditch or St Paul’s. I think St Paul’s charges £17 to go in, but then that ticket lasts 12months.
Shoreditch is great for more independent retailers and restaurants. They have the box park with loads of insane places to eat. Voodoo rays is fab. If you go there Sunday morning you could also walk up to Columbia Flower Market.