Hope this helps.. (I've removed duplicates and arranged them in zones and in a certain flow). Hope I've not left out too much details.
NORTH
Galley by the Straits - 43 Admiralty Road West (inside SAF Yacht Club)
Bottle Tree Village Food
Bottle Tree Village is located at:
60 Jalan Mempurong
Singapore 759058
Off Sembawang Road
Sembawang Eating House (Seafood Restaurant)
Tel: 6752 6953
Vanilla Pod at Mandai Orchid Gardens
Singapore Zoological Gardens.
Try "Breakfast with Ah Meng." You can wine and dine in style with Singapore's most famous primate. It is closest you can get to nature.
NORTH-EAST
Sunset Grill and Pub
140B Piccadilly, Seletar Airbase
(from Piccadilly, turn into Lambeth Walk, Hampstead Gardens, Western Ave, into East Camp, all the way to Singapore Flying Club)
Tel: 64820244
4pm to 10pm; closed on Tuesdays
Hougang Park.. overlooking "lake" / lakeside
EAST
Pasta Fresca da Salvatore at East Coast Park, next to the food centre. The tables are on the beach itself, and the food is excellent. Lovely place to go at night.
CENTRAL
Halia Restaurant - Botanic gardens.
the Cafe run by the Les Amis group at Botanic Gardens Visitors' centre
PS Cafe at Harding Road
Ridout Tea Garden along Queensway
Outdoor seating at Graze - Rochester Park
Too bad the food is disappointing.
Da Paolo and Min Jiang are also there but I'm not sure about the view/closeness to nature.
Da Paolo - 3 Rochester Park (inside the park)
The Colbar in Portsdown Road
Villa Bali (near the old SAJC) is fantastic. Lovely gardens. Wonderful space.
Villa Bali at Pasir Panjang. Opposite PSA Building.
Nice ambience to chill out and have drinks after dinner.
The Olive Ristorante
Address: Labrador Park, Labrador Villa Rd, Car Park A (opp PSA Building at Alexandra Rd)
Opening Hours: 12pm –11pm daily
For reservations/enquiries : 64792989 (ristorante), 63396833 (office)
The bar/restaurant on top of Mount Faber.
The Cliff at Sentosa.
Il Lido at Sentosa Golf Club, if you sit outside it's situated in very nice greens and there's a fabulous view of the harbour and the sea.
WEST
Sakura NA NA - Clementi Woods
NORTH-WEST
Ivy Singh's restaurant in Lim Chu Kang
Excellent curry there
http://bollywoodveggies.com/
You can walk around in their huge vegetable garden. Nice place for macro shots. Food is good also, not too expensive. Try their Fig Tea.
Petals & Leaves Bistro
Nyee Phoe (Gardenasia)
240 neo tiew crescent
tel. 6793 6500
Opening Hours:
Saturday ( 11am - 10pm )
Sundays & Public Holidays ( 10am - 6pm)
http://www.kranjicountryside.com
OTHERS
and if you are not lazy...go to the tree-top makan at JB. Really need to go up the tree!