Nothing wrong with some touristy things I indulge in them myself sometimes!
Tourist things in Central Lon I like are the Southbank - great to walk along, eat and drink anytime. The National Theatre is fantastic and you can usually get tickets for stuff there. Tower of London - tourist hotspot but really great to visit.
Places in Central I like to eat at:
Soho - Mildreds (Veggie), Polpo, Burger and Lobster, many places to eat and great to wander in an evening.
Cheaper reliable eats - Franco Manco sourdough pizza, Honest Burger,
Afternoon Tea at Savoy nice
The River Cafe not cheap so treat but nice location
Aside from well known places London is like lots of villages clumped together. I know East and North but West is a foreign country.
There are nice markets (Camden, Portobello)
Broadway Market on a Saturday is great (foody) (Bethnal Green tube). Also has nice eating places on the Market - (Market Cafe and El Ganso recommend) You can do a great walk easily from Broadway Market along Regents Canal to Angel Islington (about 40mins) lots of nice places along the canal to eat. I like Islington. Ottolengi in Islington good.
Columbia Road Flower Market also great on a Sunday (Also Bethnal Green tube, then walk to Liverpool Street via Shoreditch. Good pubs around the Market for lunch. Its all old east end (but gentrified now ). Spitalfields Market also good to vist.
Borough Market popular and the Fish restaurant there very nice to eat in
Arty - Tate Britain, focus on British Art and I love it. Barbican is also great for live performances both classical and modern, musicals. There are no
tit galleries/museums in London that I have been too.
Lots of Footy! Spurs, West Ham at The London (Olympic) stadium will have tickets. (The Aquatics Centre in Olympic Village next door to West Ham is the best pool in London to swim at. its great and cheap) Fulham FC is in a great location on the River Thames.
There are some great lidos to swim in if they like that - open water in the docks too.
Just Drive right about day trips too - Cambridge very easy from King Cross (45mins) and a great place to visit, loads if places doable in a day - York, Manchester, Canterbury
Lots of people do The Harry Potter tour from London at the studios.
It really depends what your friends are into and what time of year - there is an awful lot more..for example Hampton Court Flower Show I would strongly recommend if you like gardening and here around Wimbledon time..Hampton Court Palace itself is great to visit anytime too..
Anymore recommendations a bit too much info but if there are specific interests they have come back
I suspect
@Violetroselily is a South Londoner and will have lots to recommend