Hi SEO Team @ G5!
Since you are unable to create one large domain that houses all of the locations, I would attempt to make each of the websites as "unique" as possible. But keep in mind that unique content doesn't necessarily mean that you need to completely reword the content in different ways 250 times. Small changes can make a big difference.
There's a great (and short) video of Google's Matt Cutts talks about how Google handles duplicate content. There's also another helpful video about it here.
Matt Cutts has said, "Google looks for duplicate content and where we can find it, we often try to group it all together and treat it as of it’s just one piece of content. So most of the time, suppose we’re starting to return a set of search results and we’ve got two pages that are actually kind of identical. Typically we would say, “OK, rather than show both of those pages since they’re duplicates, let’s just show one of those pages and we’ll crowd the other result out,” and then if you get to the bottom of the search results and you really want to do an exhaustive search, you can change the filtering so that you can say, “OK, I want to see every single page” and then you’d see that other page. But for the most part, duplicate content isn’t really treated as spam. It’s just treated as something we need to cluster appropriately and we need to make sure that it ranks correctly, but duplicate content does happen."
Read more from this article here: https://searchenginewatch.com/sew/news/2319706/googles-matt-cutts-a-little-duplicate-content-wont-hurt-your-rankings
With this in mind, I do think your assumption is correct. If you make sure that any location that could be seen as competing areas has unique content, they won't necessarily be dinged for duplicated content. Unless you were trying to rank nationally, this shouldn't be a major problem for each individual website that is targeting a different location.