Good to have you on-board, @troher . Singapore’s culinary landscape is really not that hard to navigate around. I’ll share with you some of my fave spots, but you are most welcome to ask more specific questions later.
Most newbies to Singapore food would definitely want to try our street food - which are now contained in what we Singaporeans call hawker centres, ever since the Singapore government cleaned up the streets and require all street hawkers to move into these hawker centres back in the 1970s/80s. The first hawker centre was Newton, built in 1971, the same year I entered elementary school. The last hawker centre was Jurong West, built in 1986, as I was in my second-last year in university. There are currently about 110 hawker centres spread out across Singapore, feeding millions daily.
Makansutra was conceptualised by the ever-energetic and tremendously visionary KF Seetoh in 1997, and which started off to provide a guide specifically for Singapore street/hawker food, as a counter-alternative to the hoity-toity Best 100 Restaurants Guide produced by the very influential Singapore Tatler at the time. KF Seetoh and I both worked at the Singapore Broadcasting Corporation (today called Media Corp of Singapore) back in the late-80s/early-90s, but didn’t get to know each other till much later. Today, we try and catch up every chance we’ve got, and I still regard Makansutra as the best guide to Singapore dining ever.
KF Seetoh visits Penang quite a bit - seen here with Madam Beh Gaik Lean of her eponymously-named 1-Michelin-star Auntie Gaik Lean’s Old School Eatery last year.
To start off your Singapore food exploration, I’d recommend that you visit the hawker centres. The top 5 hawker centres in Singapore, IMHO, are:
- Hong Lim Market & Food Centre - must-try stalls there are Heng Kee for curry noodles, Tai Wah for “bak chor mee” /minced pork noodles, and Outram Park Fried Koay Teow for “char kway teow”.
Heng Kee’s curry chicken noodles is what I’d want if I need to choose just ONE dish to eat before I die.
I brought Chowhound’s founder & Alpha Hound, Jim Leff, here a few years back, and he cleaned up every single drop in his bowl.
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Maxwell Food Centre - Singaporeans (and out-of-state visitors) make a beeline for Maxwell Food Centre mainly for its famous Tian Tian Hainanese Chicken Rice, as well as its breakaway, bitter rival, Ah Tai Hainanese Chicken Rice.
There are a few other stalls worth exploring there, but these 2 chicken rice spots are the star attractions.
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Old Airport Road Food Centre - perhaps the No. 1 hawker/food centre for many Singaporeans, who’d journey all across the island to come eat here. The star pulls include Nam Sing Hokkien Fried Prawn Mee, Lao Fu Zi Fried Kway Teow, and Hua Kee Wan Ton Mee.
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Amoy Street Food Centre - I come here for my fave “lor mee” - Michelin-Select Yuan Chun Famous Lor Mee. Many Singaporeans come here just for the fish soup, with two rival stalls forever duking it out for the top spot: Han Kee and Piao Ji.
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Chinatown Complex Market & Food Centre - the best-known stall in this massive food complex is Lian He Ben Ji Claypot, a Michelin Bib Gourmand-listed eatery.
I come here for my own fave stall: Ma Li Ya Virgin Chicken. A must-try.
For Chinese fine dining, and Cantonese dim sum, both of which Singapore does very well. I try to avoid the very top-end, super-exclusive ones, but go for the popular ones frequented by Singaporean foodies/gourmands. My top 5 are:
- Imperial Treasure Fine Teochew Cuisine (ION Orchard)
- Crystal Jade Palace (Takashimaya Shopping Centre)
- Imperial Treasure Super Peking Duck (Paragon Orchard)
- Taste Paradise (Ion Orchard)
- Asia Grand Restaurant (Fairmont Singapore, Raffles City).
Explore Singapore’s Malay/Arab quarter, and go for its Indonesian nasi padang. My top 5 picks there are:
- Warong Nasi Pariamman for Indonesian-style rice with curried dishes.
- Kampong Glam Cafe for its breakfast options like nasi lemak and especially its ultra-delicious lontong: cubes of compressed rice cakes drenched in a piquant, turmeric-scented, coconut milk-enriched gravy.
- South Indian-Muslim prata and murtabaks from either Zam Zam or its deadly rival, Victory.
- Hajah Maimunah on Jalan Pisang - this Bib Gourmand-listed Malay lunch spot is a dining icon in Singapore, and definitely a must-visit.
- Naadhira Ismail’s Mother Dough Bakery for a taste of Singapore cafe culture.
For Singapore-style chili crabs:
- Keng Eng Kee, Bukit Merah - make sure you book well ahead, and reserve the crab dishes!
- Roland, Marine Parade Central - eight-decades-old and still going strong. Roland Lim’s mum, Cher Yam Tian, was a local food icon of sorts.
- Mellben Seafood, Ang Mo Kio - our family go-to place for seafood, since it’s nearest to where we live.
- Long Beach, East Coast Parkway - it used to be regarded as serving the best chili crab in Singapore for the longest time. Still very good at what they do.
- Seafood Paradise, Vivocity. One of my fave places to go to - mainly because of their professional service. They also got their chili crab gravy’s flavors spot-on.
- Palm Beach Seafood - another oldie but goodie.
When it comes to chili crabs, there are simply too many options, so I won’t list anymore here, although I have that urge to do so. 
No visit to Singapore is complete without a quick visit to Little India and exploring its good eats:
- Komala Vilas for South Indian vegetarian eats. Founded in 1947, as Singapore was emerging from the ravages of Japanese occupation during World War II, this is the oldest and best-known Indian breakfast spot.
- Madras New Woodlands - my personal fave dining spot for South Indian vegetarian.
- Fish-head curry from Apolo Banana Leaf - another Singapore dining landmark, and a must-try.
- Explore the food stalls inside Tekka Market Food Centre. The best-known stall is Allauddin’s Briyani.
One of the most popular dishes for visitors to Singapore - the Hainanese chicken rice. My fave spots are:
- Chicken House, Upper Thomson Road
- Boon Tong Kee (Balestier Road)
- Wee Nam Kee (United Square)
- Tiong Bahru Boneless Hainanese Chicken Rice
- Margaret Drive Chicken Rice, Holland Drive - this place was so-called because it was the famous Sin Kee chicken rice stall which used to be located in Margaret Drive, but has since moved here to Holland Drive. It decided that its old address was more recognisable to its legions of fans over the decades than its old stall name.