I think this one missed out, while working our way upwards.

Fertö/Neusiedlersee
Laponian Area
Wachau Cultural Landscape

http://www.worldheritagesite.org/categories/category69.html

Ah, I now see we have two Categores for Agriculture! They need to be merged.
We then reach a total of 18.

Fertö/Neusiedlersee
Laponian Area
Wachau Cultural Landscape
Alto Douro
Coffee Cultural Landscape
First Coffee Plantations
Hani Rice Terraces
Head-Smashed-In Buffalo Jump
Kuk
Lavaux, Vineyard Terraces
Palmeral of Elche
Pico Island
Rice Terraces of the Philippine Cordilleras
Saint-Emilion
Tequila
Tokaji Wine Region
Viñales Valley
Vineyard Landscape of Piedmont

Among these we have:
- 8 Vineyard sites: Pico seems to be the most scenic
- 2 Coffee sites (Cuba represents the early form, Colombia the later)
- 2 sets of Rice Terraces (Philippine seems to be the one to choose: outstanding example of high-altitude rice production, a pre-colonial practice & still viable today)

And the more unique:
- Kuk - Don't know if it's a great representation of PNG
- Tequila
- Head-Smashed-In Buffalo Jump - Representing the unique hunting practice of precolumbian Americans
- Palmeral of Elche
- Laponian Area - Pastoralism, reindeer husbandry
- Vinales Valley - Culture of tobacco

A number of these are also under consideration at other posts because they're cultural landscapes.
I'll bring the conclusions here:
- Climats, terroirs of Burgundy - had to choose few vineyard CLs with good architecture
- Lavaux vineyard terraces (one of the best examples in continental Europe) ???
- Pico Island (one of the most unique examples of wine growing worldwide)
- First Coffee Plantations -
- Rice Terraces of the Philippine Cordilleras
- Wachau - for the imposing abbeys (non-Agricultural reason)
- Kuk

Most of these sites I already chose in other categories.

Of the remaining, my selection is:
Vinales valley
Laponian area
Kuk

Which viticulture site to choose?
- Pico seems to be the most unique one
- I feel we need to have one or two from the main winemaking regions in Europe

My selection:

Wachau Cultural Landscape
Coffee Cultural Landscape
Head-Smashed-In Buffalo Jump
Kuk
Rice Terraces of the Philippine Cordilleras

For viticulture I chose Lavaux as it includes several European varieties of grapes and it is a magnificent landscape

Fertö/Neusiedlersee - N - always had some trouble with that one; no sure what's so special about this site
Laponian Area - N - can't really warm to this site; also wonder whether sites in Norway or Finland may be more representative of Sami culture
Wachau Cultural Landscape - Y - because of the abbeys etc.
Alto Douro - N - would probably go for Burgundy and Tokaji as
Coffee Cultural Landscape - Y - closely associated with the identity of Colombia
First Coffee Plantations - N - no if we have the Colombian site
Hani Rice Terraces - N - go for the Philippine site
Head-Smashed-In Buffalo Jump - Y - representative of native American hunting practices
Kuk - N - interesting from an archaeological perspective - seems like a niche site to me in this context
Lavaux, Vineyard Terraces - N - picturesque but would still prefer other wine-making sites as being more representative
Palmeral of Elche - N - a bit niche
Pico Island - Y - very picturesque site among the vineyards
Rice Terraces of the Philippine Cordilleras - Y - iconic rice terrace site
Saint-Emilion - N- go for Burgundy
Tequila - N - interesting but a bit niche
Tokaji Wine Region - Y - a more eclectic one amongst the major wine regions, and thus quite fascinating
Viñales Valley - Y - for tobacco cultivation, which is closely associated with Cuba
Vineyard Landscape of Piedmont - N - go for Burgundy and Tokaji as traditional sites

Wachau Cultural Landscape
Hani Rice Terraces
Pico Island
Rice Terraces of the Philippine
Saint-Emilion
Burgundy

After been to both Filipino and Chinese sites, I choose Hani rice terraces for its better preserve, bigger sites and more beautiful. Also much older since the new discovery that actually the sites in Philippines is only 300 years old!!

Summary of where we're standing now. I think this category is quite covered now.

Fertö/Neusiedlersee
Laponian Area - Represents pastoralism and reindeer husbandry, but a site hard to warm too
Alto Douro
Coffee Cultural Landscape - closely associated with the identity of Colombia as coffee-producing nation
First Coffee Plantations - (NB: I seem to be the only one that likes it so far, find it more interesting than the Colombian ones)
Hani Rice Terraces
Head-Smashed-In Buffalo Jump - representative of native American hunting practices
Kuk - seems a bit niche, but is about agriculture & only representation of PNG on the list
Lavaux, Vineyard Terraces - only Clyde so far, includes several European varieties of grapes and it is a magnificent landscape
Palmeral of Elche
Pico Island - most picturesque setting of all Vineyard sites
Rice Terraces of the Philippine Cordilleras - iconic and outstanding example of high-altitude rice production
Saint-Emilion - only one supporter so far
Tequila
Tokaji Wine Region - also only one, a more eclectic one amongst the major wine regions, and thus quite fascinating
Viñales Valley - for tobacco cultivation, which is closely associated with Cuba
Vineyard Landscape of Piedmont

Bring in from other category for inclusion:
Burgundy - vineyard CL with good architecture

Move forward to other category for inclusion:
Wachau Cultural Landscape - for its imposing abbeys

My selection:

Fertö/Neusiedlersee
Wachau Cultural Landscape
Hani Rice Terraces
Rice Terraces of the Philippine Cordilleras

In the continuing CL there are two in support of Lavaux.

Yes, that is shown in that category already and will be brought over to the general list. I take the 'highest' rank from each category from sites with multiple categories.