Here's one I don't think anybody has thought of yet: the Kerguelen Archipelago in the far south of the Indian Ocean. It has a climate comparable to the Aleutian Islands, which supported sizeable local populations once upon a time. It also has deposits of low-quality but burnable coal, excellent peat, and volcanic sulfur, lots of guano for saltpeter, and piles and piles of useful scrap metal from past ventures in the islands. Besides edible native animals and plants, it has tasty and useful introduced animals, such as reindeer (and lots of cats!); if Year 0 was in 2011 or earlier, it would also have hardy sheep and a working greenhouse (both have since been removed). Many of the local marine mammals never leave the Southern Ocean and the ones that do migrate wouldn't be heading out for months. This would give the local people time to figure out what to do about sea monsters when they did show up, presuming that they got that information before communications went down.
Kerguelen is arranged in a loose rhombus with two other subantarctic island groups, the Crozets and Amsterdam-St. Paul, plus heavily populated and much warmer Reunion Island. The three subantarctic groups support scientific bases and there is also a small French military base on Kerguelen. I happen to know that a large, well-equipped supply ship makes a regular circuit of just under a month from Reunion to the Crozets to Kerguelen to Amsterdam-St. Paul and back to Reunion again at that time of the year. This ship can stay at sea for 60 days. If Madagascar, which has jet flights to Reunion, closes its borders while the ship is in port for refueling, the crew might smell trouble and decide to go pick up everybody early. This would be more than 100 people. There would be up to 110 passengers already, mostly scientists headed to the bases to replace outgoing personnel, but also a few tourists, plus up to 50 crew depending on operations; a lot of them might choose to head out, hot-bunking as necessary, because they weren't planning to stay on Reunion that long. Or they might decide that it's got to be safer out there than on Reunion, which has too many people to feed with local resources, being largely a tourist destination. In any case, they're at sea when the satellite link goes down and the radio starts to scream. The captain gets everybody to Kerguelen, as the largest and best supplied base, and then steams around for as long as he can before returning with the news that there's nowhere to go. For all they know, the 250 or so people on Kerguelen are all that remains of the human race. Luckily there are 43 women able and willing to bear children, which is just enough to keep inbreeding at bay. With masses of data about the islands at their fingertips, they begin to plan.
In Year 90, the population has grown to about 650 in several settlements around the islands. The new settlements are composed of long, narrow houses made entirely from dry-laid local stone and surrounded by networks of high and low stone walls. The walls are used to create microclimates where hardy vegetables may be grown, keep the wind off tiny plantations of conifers nurtured from the only two trees in the islands during Year 0, and also keep out any stray seal-beasts and sea-lion-beasts. Luckily these are just as slow and clumsy on land as uninfected pinnipeds. Between the hunters who shot meat for the scientific base and the personnel at the military base, there were plenty of guns in the early years. The military established regular patrols, shooting all beached beasts before they could infect anything on land. They are rare these days and the cats provide plenty of warning if they come ashore. Sea monsters were a tougher foe, but black-powder cannons are just feasible using local resources, so they also get shot on a regular basis if they approach the shore too closely. The weather is more of a hazard than beasts these days.
The people live plain but fairly comfortable lives with coal and peat fires heating their new stone homes. (The original wooden and metal buildings were largely unusable after imported fuel ran out and are used for raw materials, as is the hulk of the cargo ship that rescued so many people.) They make kayaks and coracles from leather with frames of driftwood or carefully rationed conifer wood, and they dress in penguin skins and wool, sleeping between wool blankets on leather mattresses stuffed with sweet herbs. Between gardening, hunting, fishing, and livestock, they eat quite well. They are experimenting with both parchment and quipu (from the Inca Empire, a way of encoding information using knotted cords--which can be made without killing livestock) to preserve their knowledge before the original books crumble away. Besides the precious monster-killing cannons and a few muzzle-loaders, they don't have any high-energy technology anymore, but they do remember important things like germ theory and condoms made of animal gut. They estimate that with care, they can grow their population to just over 2,000 people.
In Year 90, a ship flying the Malagasy flag heaves to just off the main settlement and begins to signal...