Roundhay Park came fourth in the nationwide survey, polling 19 per cent of the vote.
Topping the list of 20 great family picnic spots was Three Cliffs Bay on Wales's Gower peninsula, followed by Padley Gorge in the Peak District. Third was another Welsh coastal spot, Aperporth Beach, and fifth was Kyoto Gardens in London's Holland Park.
Roundhay was the only Yorkshire location to make the list, which was commissioned by digital entertainment service DisneyLife.
Shortlisted picnic spots were judged on criteria such as views and surroundings, accessibility, facilities and parking. Two thousand British parents then voted for their favourites.
Other popular choices were:
6. Jubilee Gardens, Beer, Devon
7. Richmond Park, London
8. Whiterocks Beach, Portrush, County Antrim, Northern Ireland
9. Studland Beach, Dorset
10. Dolbadarn Castle, Snowdonia, Wales (16%)
11. Tarn Hows, Lake District
12. Stone Circles at Avebury, Wiltshire
13. Ashridge Estate, Hertfordshire
14. Flint Castle, Flintshire, Wales
15. Dovedale, Peak District
16. Birches Valley Forest Centre at Cannock Chase Forest, Staffordshire
17. Christ Church Meadow, Oxford
18. Boden Boo woodland, edge of the River Clyde by the Erskine Bridge, Erskine, Scotland
19. Bewl Water, Lamberhurts, Kent
20. Galloway Forest Park, Dumfries and Galloway, Scotland