Singapore Lodging !

When we were in Singapore we stayed at a posh hotel because I had just inherited some money, but we saw some really nice looking small hotels in the Little India section of Singapore. We went into one to get info and it was not at all expensive. If you research hotels in that small part of Singapore you might find a gem to your liking. I loved Singapore. Lucky you to be going there.

When do you plan to go, how long do you plan to stay, and what's your budget?

you may want to look at Park Avenue Clemenceau, we stayed there earlier this year and found it very good it suited all our needs, taxi at the door ( which are inexpensive) free breakfasts( most days) plus it was an apartment.pool, supermarket and cafe below, we would definitely stay there again.
hope this helps.

We are in Singapore the last week of January and usually enjoy an RS type B&B, but this isn't Europe.

I read that the Orchard Road area is quieter, but are we closer to the MRT if we are in the Colonial district or Little India ?

May I suggest you contact the Singapore tourist office?

These serviced apartments might be of interest if you're going to be there a full week: http://www.stayfareast.com/en/serviced-residences/orchard-parksuites.
We lived there for 3 years back when I still had to work for a living. Their rates for a one bedroom apartment are reasonable (by Singapore standards), although they do require a 7 night stay. And the property itself is terrific - 5 star all the way with every amenity you can imagine, and it's as quiet as a church despite its central location. Having a kitchen will allow you to save money by being able to cook at least some of your meals in. Then you can splurge a bit in the evenings if you so choose. Their concierge service can help arrange local tours, although striking out on your own is pretty easy given the compact nature of the city-state.
The location can't be beat - across the street from the Orchard MRT station (the metro), and a few feet from the heart of Orchard Boulevard. The MRT is cheap and efficient, though as has been mentioned the taxis are also very cost-effective.
Know that although it's always hot and humid in Singapore the last week of January is historically the hottest time of year.

Thank you for the guidance ! And, yes, I will contact the tourist office.

Singapore rapid transit is both convenient and efficient. The home website covers "trains" (i.e. LRT and subway trains) and buses. It includes a trip planner. I think some if not all services can be accessed from a smart gizmo, my term from cellphone. Wikipedia, frequently useful for DIY research, offers explanations and includes links to the services.
https://en.wikipedia.org/wiki/Mass_Rapid_Transit_(Singapore)

Thanks for sharing !!

A bit of a splurge, but I loved the Fairmont Hotel. I think they had the most comfortable bed I’ve ever experienced in a hotel. My room had an amazing view. The hotel is right across the street from the famous Raffles Hotel, and built over a food court with some great options - for me, a Vietnamese sandwich and coffee one day, and wonderful Chinese dumplings another day. It was walking distance to some sights (if you can stand the heat) and right above a subway station to get most anywhere.

I think I got a discount on the room by joining their loyalty club. I had a late evening flight out of Singapore, and they gave me the free use of a “day room” after I checked out. I was also able to shower and freshen up in their spa (also free) before heading to the airport.

Really enjoyed my time in Singapore. Hope to return one day. Don’t miss Gardens by the Bay, a most unusual and amazing place. I went in the evening when it was cooler and pleasant. Have a great time!

Sentosa Island is accessible by cable car and worth an afternoon visit.