you don't say what you like and you don't say what is "touristic" in your opinion. But here are some suggestions as a londoner.
1. evening: some alternative comedy or a young band or jazz.
2. go clubbing in shoreditch, combine with indian meal on brick lane.
3. sunday: the east end markets - spitalfields, brick lane, columbia flower market
4. stroll on hampstead heath or richmond park
5. walk along regent canal. reocmmended - new north road to camden go off the road in Islington for the small market (f it's Sunday afternoon)
6. saturday - borough food market + stroll on south bank.
and don't slag off some of the tourist attraction, especially art & culture and some of the greatest architecture in europe.
feel free to write me with further pointers to your taste and dates (dates influence a lot)