I've lived in London for 18 years... when I was a student I lived in Kings Cross for 4 years.
I like the burger, wagamama restaurants - but personally I'd try to stay away from these chains if I wanted to see a more interesting side to London.
Definitely go eat at Brick Lane, which is to the East of 'The City'. There are loads of cheap Bangladeshi/Indian restaurants (30+) which are good quality - the place has a really fun vibe, and the restaurant owners are out on the street offering deals to would-be customers. The area is interesting too - the old East End of London. If you're out late, go to the North end of Brick lane, where two 24x7 bakeries sell bagels with salt beef at all times.
Around the area to the North West of Brick Lane is Hoxten Square. This is an art / club / bar district, and it's the place to hang out in the evening. Just go from bar to bar and see what's happening. It's only about 10 minutes from King's cross by bus when you need to get home.
Go North West from Kings Cross and you get on to Islington High Street / Upper Street - this is a fantastic bar/restaurant district. Some great restaurants here - great Argentinian, Cuban restaurants. Go to the Bierodrome for a selection of hundreds of great Belgian and continental beers (
http://www.belgo-restaurants.co.uk/ )
Down to the South West of you is Tottenham Court road with it's electronic shops (prices aren't great)... the roads to the West of it are called 'Fitzrovia' - and this is a thriving bar/restaurant district, with lots of people out on the streets by the pub when the weather allows (lots of English pubs now have outdoor heaters so cold weather isn't a problem). Find Charlotte street on the map and start there.
I recommend Borough market (
http://www.boroughmarket.org.uk/ ), especially on Friday / Saturday. Lots of food for sale, and you can buy BBQ chorizo sandwiches, fresh roast pork, great fish, falafel, frankfurthers etc. Good for lunch. The George pub is great and it's very near (
http://www.beerintheevening.com/pubs/s/43/434/George/London_Bridge ).
Other fun places:
On Edgeware Road there's a big middle-eastern community. Some fantastic kebab restaurants, and you can sit out and smoke a 'hookah' pipe. (Walk North from Marble Arch station towards Edgeware Road station)
By Queensway tube is a great restaurant district (some good Japanese and Chinese food - I like 'The Magic Wok' - the guy running it is really friendly). The Whiteleys centre is there, which contains a good multiplex cinema.
Down in the centre of the West End is China Town. There's a small cafe down one of the back streets called 'The C and R Cafe' which sells brilliant cheap Singapore/Malaysian food. The Roti Canai is fantastic (flat breads with tasty gravy to dip). I also like the Nasai Lamak (
http://www.london-eating.co.uk/5970.htm )
South from Kings Cross down Judd Street is a great pub - the Lamb (probably 15 minutes walk)
http://fancyapint.com/pubs/pub77.html