Professionally trained chefs tend to be found in the up-market resorts rather than public cafes. 
To experience proper Daintree dining stay a night or two: best deals
Daintree Accommodation

ss Rob's place

Pies baked fresh daily
3 Stewart Street Daintree Village

Julaymba Restaurant

Not open for Lunch
Daintree Eco Lodge & Spa
Phone: 074096100

Big Barra

BIG Barramundi Garden

Breakfast and lunch
Daintree Village
Phone: 0740986i86

Daintree Tea House
Longest continuously owned restaurant in Daintree and often #1 in Tripadvisor
Phone: 0740986161

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The Daintree area lends it's self to picnics and Bar-B-Q's with free electric Bar-B-Q's at Wonga Beach & Daintree Village.
Picnic places can be found throughout.

picnic lunch

Daintree Village Hotel
Daintree Village
Phone: 0740986146

Caltex Wonga Take Away
Mossman - Daintree Road, Wonga
Phone: 07409877616

North of the Daintree River.

Turtle Rock Cafe
Turtle Rock Cafe
Cape Tribulation
Phone: 0740980185

Daintree Flavours
Cow Bay Hotel
Phone: 074098901

Mason's Cafe and Take Away
Cape Tribulation
Phone: 0740980016