High ground cannot be (re)supplied easily. Soil and air is thinner, erosion can be a real concern, water runs off high ground so sourcing water is always harder. Building a base can be tough if material like wood isn't available up there (mountains can be wooded or it can be barren), or if the terrain makes it hard to log compared to on lower flat ground. And camping on high ground is absolutely worse. It takes many years and a lot of manpower to make a truly functional base on high ground. Fact is, you won't find many modern military bases on high ground. Not even many from industrial era. These survivors won't have the luxury of time and manpower to build and many of them are civvies women and children. And it wouldn't solve the fundamental problem of resupplying. History is filled with cases of high ground forts/castles being sieged until they fall from lack of supplies. Heck even forts/castles/cities on low ground have been sieged until they fall from lack of supplies. If you've never been in the military before, I suggest you do not assume that high ground is better. That's like a common misconception, as well as theory from bygone eras long ago, that fiction helped reinforced.
As for a basin, the easier access points will be limited by nature, and there will be watershed areas where water gather so water supply should not be an issue, which is pretty important for any base. There are probably many other advantages as well but I'm not really an expert on the topic as I was never a high level officer nor involved in military planning. But that anecdote of the commander losing by naively choosing a high ground to set base, was shared by the veterans with us back then precisely to break the common misconception that high ground is supposedly better. I also used to unquestioningly think high ground is always better.