Singapore is a Gourmet's Paradise. This has been narrowed down as the information could be overwhemling for a newbie to Singapore.
Seafood
1) East Coast Seafood Center - a few restaurants all in one place along the water (some are on the other side which is not on the water), the more popular ones are Jumbo, Red House and Long Beach. Dishes to order are baby kai lan or sambal kang kong, chili or pepper crabs, drunken prawns, bamboo clams, bread for dipping up the sauces. No frills service, don't expect elegance and finesse
2) Famous hawker centers - eg. Newton or Chomp Chomp, recommended dishes are BBQ sambal sting ray or squid
3) Esplanade - No Sign Seafood would be the best choice here. Newton food centres can be too touristy. Try Bedok Hawker Center at bedok MRT.
4) Boat Quay - able to dine outdoor right by the water
Hawker Centers
1) Newton Food Centre (nearest MRT: Newton)
2) Maxwell (Nearest MRT: Tanjong Pagar)
3) Chomp Chomp (aka Serangoon)
4) Zion
5) Adam Food Centre
6) Lau Pa Sat
Note : you can find a food court in almost all the shopping malls or office buildings in town and they are usually all pretty good. Some are more local (eg. Far East Plaza's 3rd floor with each individual shop) while others (eg. Tanglin Mall's), are one big food court with individual stalls, more cafeteria style. Also, a lot of the older ones had been updated for cleanliness and style (blend of hawker center and air conditioned food court) and the new ones like Glutton Bay are made of the new style hawker dining.
Vegetarian
1) 7 Sensations - Little India, Madras Street, Holistic Vegetarian Food with good variety of cuisine
2) Kaoyi - on Lavender Street, local and chinese dishes
3) Fortune center - next to Guan Yin temple, dishes that chinese monks and nuns would usually dine on
4) Maharaja - on Cuppage Terrace
5) Komala Villas - very popular as the food is good
6) Bombay Woodlands - in Tanglin Shopping Center, good lunch buffet and very reasonably priced esp. for an in town location
7) Lu Qing Qing - in Chinatown, good home made noodles
8) Original Sin - in Holland Village, Mediterranean cuisine
9) Lao Di Fang - a few locations in town
10) TGIF - if you feel like having a burger, try the garden burger
11) Kingdom - at Suntec City, noodles are good
High Teas
1) Raffles hotel - can't miss the most famous one in town
2) Four Seasons hotel
3) Holiday Inn Atrium - weekends only
4) InterContinental hotel - weekends are buffet style
5) Mandarin hotel - Mezzanine Lounge but on weekends and public holidays u can also have high tea at Top of the M
6) Marina Mandarin - weekends and public holiday
7) Marriott
8) Goodwood Park Hotel - similar atmosphere to Raffles choice of an Asian or English high tea
BUFFETS:
1) Furama RiverFront Hotel - Peranakan (mix between malay and chinese)
2) The Conrad Hotel, Oscars Buffet - International
3) Four Seasons Hotel - daily theme
4) Hilton - different theme daily
5) Holiday Inn Atrium - curry and local cuisine
6) Holiday Inn Park View - International
7) InterContinental - Seafood & Med. cuisine
8) Marriott - international
9) Pan Pacific - Steamboat and international, for weekends you have a choice for really good Japanese buffet in Keyaki restaurant
10) Swissotel Merchant Court - Peranakan and International, very popular as it is very reasonably priced and quite a selection
11) MELT at The Mandarin Oriental Hotel- awesome variety and quality
12) Straits Kitchen at The Hyatt Hotel- Lots of Variety and great way to try local food at a luxurious setting
Other cuisine
Grill - not to be missed is the famous Raffles Grill, has a good wine list, Harbor Grill at the Hilton is also very good .
Indian -must order the Fish Head Curry- Muthu's Curry at Race Course Road, Little India or Samy's Curry at Dempsey Road (close to the Botanic Gardens). Very reasonable prices and great food!
Indonesian - Rice Table (they also have a buffet dinner choice).
French - L'Aigle D'Or at the Berjaya hotel is excellent, Casual French restaurant in Little India called French Stall is wonderful, Les Amis is pricey and over-rated especially by those who have never tasted really superb French cuisine in France.
Hakka - Moi Kong (unique Chinese cuisine, not very common, special dish is suan pan zi)
Thai- Patara Thai Restaurant at Tanglin Mall or at Raffles Plaza Hotel - Excellent food and service, great weekend lunch buffets
Nasi Padang - Rendezvous is the most well known and popular Hainanese Chicken rice - most famous and most expensive is the Chatterbox at the Meritus Mandarin hotel, Unfortunately, Chatterbox Chicken Rice is not so nice now since the 100% ginger sauce was mixed with spring onion and turned green in colour. Five Star at Bukit Timah is pretty good, Margaret Drive (Sun Kee), Wee Nam Kee (Thompson Road), IBM Towers (2nd floor) and Hainanese Delicacy at Far East Plaza.
Satay - Lau Pa Sat, Satay Club, Clark Quay
Crossroads at Marriott Hotel, Corner Orchard and Scotts Rds - great menu - something for everyone with healthy choice section as well
Dining with a view/romantic restaurants
1) Sentosa Spa and Resort's BBQ Seafood - great view of the Island all lit up at night, over the water as well as right by the pool
2) Au Jardin Les Amis - Set in the beautiful and serene Botanic Gardens, in a very nice colonial building - overpriced
3) Flutes at the Fort - very romantic esp. at the veranda, dining outside is magical but save room for desserts at this place !
4) Hai Tien Lo - view of the harbor if u like chinese food
5) IndoChine Waterfront - popular and trendy
6) Top of the M - famous revolving restaurant has the Orchard area night view - city but no more smoky dry ice effect with the chocolate balls that come with coffee. Also no more tableside flambees which is a wrong move on the part of the restaurant
7) Jewel Box - at Mt. Faber, dining outdoor, overlooking the great view down below
8) LightHouse - good food and view already closed down.
9) Keyaki - set in a beautiful Japanese garden\
10) Equinox - has the be the best view due to its location and height, both city and harbor view of the lion city but food is not that good.
11) Jaan - posh/swanky restaurant
12) Graze at Rochester Park- beautiful and great food
13) Halia - near the ginger garden in the Botanic Gardens RiverCafe - Robertson Quay
Champange Brunch
1) Mezza9 at the Grand Hyatt
2) Ritz Carlton - Moet & Chandon is the champange of choice
3) Four Seasons - Veuve Clicquot lovers beware - free flow for S$30 more than the normal price
4) Hilton Hotel - a good one for family as they have a kids' corner !
5) Conrad Hotel - accompanied by live Jazz !
6) Fullerton Hotel- Try the Chocolate Buffet!
Note : a lot of other hotels have normal brunches eg. Shangri La's The Line has an outstanding buffet spread, there are specialty buffets eg. Children's buffet at the Grand Copthorne watefront, adults have to be accompanied by at least one child, Brunch and plunge at the Rasa Sentosa, Big breakfast buffet at the Conrad serving all types of breakfast items from all over the world, don't forget for chocolate lovers, you have the chocolate buffet at the Fullerton, simply decadent !

