What is the best vegetable to plant after growing potatoes for a couple of years?
Was thinking of just letting the patch be fallow this year, but perhaps there is something better to do there.
Potatoes take most all the nutrients
I'd throw on some horse manure, rototill it in & let it go fallow a year.
The classic answer is to rotate potatoes with legumes, an let the legumes set nitrogen, while also tilling in some manure. People have variable opinions on how effective non-native crops are in Alaska at setting nitrogen. If you are in Whitehorse, your weather might be similar to Fairbanks, and in the warmer soils in Fairbanks (up in the hills) it appears that pole beans do set nitrogen, especially if you use an inoculant. I'd grow Fortex, Scarlett Runner or Noreaster pole beans, if you don't have something just north of that row that you don't want to shade.
Your mileage may vary.
If Whitehorse is warm and dry (like Fairbanks) you could grow bush beans, but I've never seen much evidence of bush beans setting nitrogen. Still, they are good for the soil.
I wouldn't let it go. I have found letting things grow wild makes it more difficult on weed control the following years.