Here is a list of pet friendly restaurants in Cape Town. This information is current mid-2015. Restaurants can change policies so a quick phone call beforehand is always recommended. Most of these have garden/decks where people with pets are allowed. ie it is outdoors.
Check first before you turn up on a freezing winter night to find you're sitting outside or outside isn't open due to the weather.

South Peninsula - Noordhoek Pet Friendly Restaurants

The Red Herring
Tel: (021)789 1783
Address: Beach Road, Chapman's Peak Noordhoek
Web: The Red Herring
Alfresco dining on the deck or in the garden areas. A casual pub styled event. The food is good. Dogs allowed on the deck/garden area.

The Foodbarn
Tel:021 789 1390
Address: Noordhoek Farm Village, Village Lane, Cape Town, 7979
Web: The Foodbarn
Fine dining style food in a casual environment without the silver service. The food is civilised without being pretentious,
that is to say it has natural taste, smells and textures, and much character.

South Peninsula - Glencairn Pet Friendly Restaurants

The Glencairn Lodge and Backpackers
Tel: (021) 7820315
Address: 12-14 Glen Road, Glencairn, Simon's Town, 7925
Web: The Glen Lodge Bay Cafe and Restaurant
Tel: (021) 786 2105
Address:134 Main Road, Glencairn, Simon's Town, 7925
Web: Dixies Restaurant

South Peninsula - Muizenberg Pet Friendly Restaurants

The Blonde and Beard
Tel: (021) 788 1569
Address: Ground Floor, Balmoral Building, 25 Beach Road, Muizenberg
Web: The Blonde and Beard

Hout Bay Pet Friendly Restaurants

Tel: (021) 790 1876
Address: 1 Beach Cres, Scott Estate, Hout Bay
Web: Dunes
People with pets can sit in the garden and on the deck.
Suikerbossie Restaurant
Tel: (021) 790 1450
Address: 1 Victoria Drive, Hout Bay
Web: Suikerbossie Restaurant

Southern Suburbs - Wynberg Pet Friendly Restaurants

Cafe Verdi
Address: Chelsea Village Wynberg
Tel: 021-762-0849
Web: Cafe Verdi

Southern Suburbs - Constantia Pet Friendly Restaurants

Tel: (021) 794 7747
Address: Spaanschemat River Rd, Constantia
Web: Peddlars
Pets can sit outside in the courtyard.

Tel: (021) 794 8334
Address: Shop 12, High Constantia Centre, Constantia Main Road
Web: Pastis

Tel: (021) 794 4696
Address: Shop 1 and 2, Constantia Courtyard, Constantia Village
Web: Melissas

Tel: (021) 794 1143
Address:  Groot Constantia Wine Estate, Groot Constantia Road, Groot Constantia
Web:  Simons

La Belle Cafe, Alphen Hotel
Tel: (021) 795 6336
Address: Alphen Drive, Constantia
Web: La Belle

Southern Suburbs - Claremont/Harfield Pet Friendly Restaurants

The Loco Lounge
Tel: (021) 671 6054
Address: 58 Surrey St, Cnr 2nd Ave, Harfield
Web: Loco Lounge

Southern Suburbs - Newlands Pet Friendly Restaurants

The Gardener's Cottage, Montebello Design Centre
Tel: (021) 689 3158
Address: Montebello Centre, Newlands Avenue, Newlands
Web: Gerdener's Cottage

Southern Suburbs - Rondebosch Pet Friendly Restaurants

Rhodes Memorial Restaurant
Tel: (086) 110 6417
Address: Rhodes Avenue, Cape Town
Web: Rhodes Memorial Restaurant

Atlantic Seaboard - Camps Bay Pet Friendly Restaurants

Twelve Apostles Hote
Tel: (021) 437 9029
Address: Victoria Road, Camps Bay
Web: 12 Apostles Restaurant

City Bowl Cape Town Pet Friendly Restaurants

Cafe Paradiso
Tel: (021) 423 8653
Address: 110 Kloof St, Gardens, Cape Town
Web: Cafe Paradiso

Company Gardens Restaurant
Tel: (021) 423 2919
Address: 15 Queen Victoria St
Web: The Company Gardens Restaurant

Marias - Dunkley Square
Tel: (021) 461 3333
Address: Dunkley Square, 31 Barnet Street, Gardens
Web: Marias Restaurant

Tasha's V&A Waterfront
Pets can sit outside with guests.

West Coast - Melkbos Pet Friendly Restaurants

Die Damhuis Restaurant
Web: Die Damhuis

Castella Amare
Web: Castella Amare

If anyone knows of more pet friendly restaurants in Cape Town, please drop me a note at info at holidogz dot co dot za so that I can add to the list.