If one does not mind staying a little further away from the city centre, in the suburb residential districts, the experience can very pleasant. There are food peddlers and small tradesmen who will sell their offerings or wares in the sois, although there is already every convenience available. Some areas even have night watchmen who patrol and announce the time through the night. Some areas are very updated, and resemble Holland Village, with gentrified establishments like gyms, cafes and supermarkets sharing the street scene with hawkers and markets.
Good advice.
It's like Singapore. There is really no need to stay in a hotel on Orchard Road. If one is adventurous enough, he could stay in Chinatown. If the government allows it, tourists on a budget could even stay in Ang Mo Kio, Toa Payoh, Jurong etc for a true Singaporean experience instead of only seeing big signboards everywhere screaming Chanel, Louis Vuitton, Prada etc...from shopfronts in Orchard Road.
With the MRT, it is so easy to move around, and seriously, the hotel room rate on Orchard Road might be say $100-150/night whereas you pay maybe $30/night on Airbnb in a HDB room (provided it is allowed), and the difference of $70-120 can more than pay for MRT rides, food, entrance fees to the zoo, Sentosa theme attractions...and even shopping.
So, I think there is no need to stay in the heart of the shopping district with the BRT making travel so fast and easy.....and so cheap. And as you said correctly, the experience away from areas which cater more to tourists is really what anyone should go for if we want to understand a country. But it's not for the fainted hearted, who tend to imagine all kinds of violence and crimes in their mind...when none exists or when it's not as bad as they imagine. Sadly, most Singaporeans belong to this group, and most have no guts to venture out far. If they do, they only go with organised tours by Chan Bros, SA Tours, etc...and in this aspect, I have to give it to ang mohs who are more daring.