Hi Aquila -- It sounds like your uncle would prefer more outdoors activities, walking around soaking in the atmosphere, so it will probably less difficult to find things to do than you would first think. Going to Piccadilly Circus might be 'touristy' but walking down Regents Street to St James Park and passing though Piccadilly Circus seems less so to me.
Will your uncle be in town on 12 November? That's the day of the Lord Mayor's show when the Mayor of the City of London is inaugurated. The parade is unique and not to be missed. All the city guilds take part as well the armed forces. Lot's of horses and pageantry:
http://www.lordmayorsshow.org/Broadway Market in Hackney on Saturdays -- more local and laid back than Borough Market and you can combine this with a walk along the Regent's canal back to Angel, which might also be of interest.
http://www.broadwaymarket.co.uk/I agree with the previous poster that the Tate Modern is worth a visit for the building alone and if you arrive by walking over the Millennium Bridge it adds something extra, plus you can take in St Paul's, even if you don't go inside. There are balconies overlooking the Thames on the upper floors of the Tate.
Though you said he does not want museum, you’ll need to have something indoors to do in case the weather is crap. Sir John Soane's Museum may interest him:
http://www.soane.org/It can only be described as an historical house, crammed with 'stuff' -- and it's free admission.
I had a bias against guided walks for a long time (mainly because of the ‘touristy’ thing) until I went on one with work colleagues and I have to say I really enjoyed it. It was a Shakespeare and Dickens walk from
http://www.walks.com/, which has many other to choose from. The guide I had was very theatrical and very entertaining. The prices are less than a tenner and no reservations, you just show up.