I completely agree with you that for a first-timer to any particular place, we would naturally want to do the touristy things. There's nothing wrong with that, and in our first trip to Paris in 2005 for three days, we did mostly touristy things too. But the key is to try to squeeze in at least one or two non-touristy things and leave out one or two touristy things. For example, in our first trip, we did Chateau Versailles (one day), Louvre (half-day), and for the other one day, we covered briefly Montmartre, Tour Eiffel, Champs Elysees and the Arc du Troimphe, and Notre Dame. That's exactly the thing I want to dispel; we should try to come away from the Ten Year Series mentality or the "Recommended things only" mentality; that's not the way to do touring; safe yes, but completely boring!
But we made time for the non-touristy things, and for one evening, we explored the St Michel area for good and cheap food and we were rewarded for the cheapest set dinner we found in France (yes surprise surprise it was in the most expensive city in France!), but for EUR 7.95 it was surprisingly good.
On another afternoon, we strolled around the romantic Jardin du Luxembourg which was very nice; we also had dinner at an off-the-beaten path with the most memorable coffee we've ever had in our life. It's these little things I feel that make the trip enjoyable; not the touristy things, which we should of course see, but not spend 100% of the time doing.
We've since gone back once more to Paris (last year) where the only touristy thing we did was to see the Centre Pompidou; the memorable thing for us was to walk around Marais and Bastille, and the Bastille street market! If you needed advice on non-touristy things to do, we could have given you some. But it's ok, I think you were set on doing only the touristy things and nothing else. Perhaps you could share with us about your memorable experiences in Paris?
This year being our third time in Paris, the only touristy thing we are going to do is to visit the Musee D'Orsay. No Moulin Rouge for us, and nor do we plan to go up the Tour Eiffel.
In fact, we did entertain a Swiss friend who came to Singapore for just one day in February, and the only touristy thing we did was to see the Esplanade and Fullerton hotel, and (gosh!) Merlion park; as well as a short stroll through Chinatown. He found the weather completely unbearable though (as I still do) and we spent the rest of the time in Crystal Jade and Long Beach seafood, eating of course.
Gosh I don't see why I would want to bring any tourist to Toa Payoh (except maybe there's a good food centre I don't know about?); a good less-touristy place I might consider would be Boat Quay / Clarke Quay, Geylang for the food before midnight, Labrador Park, Ghim Moh Food Centre, and Holland Village!
Just my 2 Euro cents worth. Everyone has a different philosophy of touring and there's no right or wrong, just a healthy sharing of viewpoints.