So, what sort of post-apocalytic wasteland are we looking at here? Is this a frozen wasteland, only just starting to emerge from the nuclear winter? Or a burning hot desertified wasteland, with little to no rainfall, a depleted ozone layer and global warming pushed over the edge? Because if it's the former, then might I suggest Durvillaea antarctica, or Southern Bull Kelp (also known as "Rimurapa" by the Maori, "Rimuroa" by the Moriori, "Cochayuyo" by the Quechua and Aymara, and "Collofe" by the Mapuche). This variety is already harvested as a food delicacy in Chilean cuisine. The vast majority of harvesting right now, in the present day, is for the purpose of extracting alginates (agar and carrageenan, both of which would also be very useful in their own right); but it has some of the highest potential yields of any crop, thanks to its extremely fast growth rate, high calorie count, high protein content (enough to replace meat altogether in some native Chilean diets) and an extremely high mineral content (enough to also serve as an extremely useful green fertilizer- albeit also with a very high salt content). Here's a bit of data about the potential harvest available to be reaped:
The approximate composition (% dry weight) of Durvillaea antartica
(Cham.) is similar for the frond and stipe, being 28% ash, 3% protein,
ca 1% lipid, less than 10% acid-soluble carbohydrate, and 60%
acid-insoluble carbohydrate. The holdfast differed by being 22% ash
and 66% acid-insoluble carbohydrate The energetic level of all 3
components was ca 13 kJ (/g dry wt). and ca 17 kJ (/g ash-free dry
wt). The relative proportion of the 3 plant components varied little
for plants having stipe diameters ranging from 10 to 40 mm, being ca
8, 3, and 89 % wet wt, and ca 10, 4, and 86 % kJ, for the holdfast,
stipe, and frond, respectively. Maximal density found in summer was
471 individual plants/sq m, 226 kg wet wt /sq m, and 457 000 kJ/sq m.
To put this in context- most modern countries have cereal yields equivalent to 5 tonnes per ha. From the calories delivered to the food system from cropland hectares, we calculate the number of people who are fed a nutritionally adequate 2700 calorie diet per day, considering 41 crops on 947 million hectares of cropland, and show that present day production of raw plant calories is adequate to feed 10.1 people/ha.
In contrast, even when growing in the wild, largely uncultivated (with the study above having taken place in the waters of the Kerguelen Islands, otherwise known as the Desolation Islands, one of the coldest and most desolate places on Earth), Durvillaea antarctica delivers a maximum yield equivalent to 2,260 tonnes per ha. That's a huge difference. Even when we look at the lowest cited figures for average crop yield (Mean standing crop of 123.5 tonnes/ha of shore, with values varying from 47 tonnes/ha on steep shores to 190 tonnes/ha on wide flat reefs, on the East coast of NZ's South Island- with individual plants producing one crop annually, and with at least two years required for new plants to become fertile), that still sounds like it should be more than sufficient to potentially kick-start a post-apocalyptic agricultural base.
Going by the nutritional values of the Durvillaea antarctica samples from the Kerguelen Plateau, that'd equate to a yield of 2,002,123 kJ per wet ton. From this we can calculate that the annual wet harvest required to sustain a single adult individual on a 2700kJ per day diet (985,500 calories per annum) would be just over 487kg, translating into a dry harvest of only 75.5kg/annum. I know, it sounds ludicrously small- how can you get 2700kJ from a daily intake of only 207g per day? But when the crop delivers 13kJ/g, the math all adds up. There's no denying that the seaweed has exceptional nutritional value- it's effectively the closest real-life equivalent to Soylent Green in existence, except that it's solid, orange, and has a texture like meat, with harvested Cochayuyo traditionally being preserved by being sun-dried (though it can also be freeze-dried) and then softened by soaking in a dish of water- with the expression "remojar el cochayuyo" (literally, "to soak the cochayuyo") also used in Chilean Spanish to refer to sexual intercourse.
With a biannual harvest, using the very lowest estimate of 47 tonnes/ha, that'd still be adequate to feed roughly 48.2 people/ha- that's almost five times the population density which can be sustained by modern day land-based crop harvests, and enough to allow a relatively densely populated fallout shelter to feed its population even with a relatively small amount of arable land (or indeed, none whatsoever, so long as they have a large and enough body of salt-water to grow it in- or even terraces of their own filtered urine, if they were either sufficiently desperate or not squeamish at all). And studies now show that this crop can also be readily used for the relatively cheap, simple and easy production of biofuels such as ethanol, which would doubtless also be critical in a post-apocalyptic environment, fighting to survive through a prolonged nuclear winter period. As for its hardiness and cold-tolerance, well- given that it literally survives, and thrives, along the coastlines of Antarctica, you can't imagine nuclear winter in the American southwest giving it any trouble...