Aside from militarism, there actually are other qualities to be admired;
*they were way ahead of the curve on gender equality. If you're going to be a woman in the Classical western world (something that affects roughly half the population according to my research) it would probably be your top option. Assuming, of course, that you're a citizen.
*Unlike Athens et al, they remained pretty stable and self-determinist for centuries. The Golden Age of Athens lasted roughly 1-2 generations. Sparta's run lasted waaaaay longer, like to a double digit factor.
* as can be said for, say, Republican Rome, within the strictures of their class divide, they were remarkably egalitarian. It's a huge caveat, obviously, but in comparison with it's contemporaries, it still stands remarkable. Athens had many more monarchs, tyrants, oligarchs in the true sense, etc. during Sparta's run of titular dual monarchies but really a restricted pseudo-collective.
* If you're a nationalist...I am very much not...they are an extreme example of state-before-individual. Probably the most extreme. So if you're constructing a nationalistic society, they will almost invariably serve as a model.
*If you are a non-materialist...I very much am...they are an extreme example of society wherein personal possessions and wealth had little to do with your status and/or power. As with anything else, this blade cuts both ways and there are troubling concurrents, but the degree to which material selfishness was a non-factor is IMO quite admirable.
I could cite more, but the real reason Sparta is so admired is IMO Athens and what I call the Intro-Psych Apotheoisis. Ever taken 1st year psych, or had a friend or w/e who has? These are people walking around avidly aware of the shingles falling from their eyes, of the possession of a New Truth that helps explain all previously confusing Life Problems. They are not necessarily giddy with it, for some it's an extremely depressing experience, but they are almost all feeling their own state of Revelation. Sparta is like that re: Athens. If, like most people, you only study the basics of Classical history, you will think Athens is the bees knees in Old Greece. But once you scratch the surface and get into the real stuff, you begin to understand that Athens' supremacy was extremely ephemeral and not terribly supreme; it lost the only war (with Sparta) it fought at it's zenith, and Sparta reigned the unquestioned leader of Greece for centuries before that, and really only began to slip a Leuctra.
More, you will around the same time begin to understand that Serious Historians have understood this for a long time, that Sparta....not Athens...has served as the model for many more (often terrifying) attempts at utopian construction than Athens ever did, and that in fact Athens often served as a cautionary tale for the maelstrom of instability that comes with democracy. They say a little bit of knowledge is a dangerous thing, and in a way Discovering Sparta can be that.
Which is not to discount the reality of it's greatness, in a practical sense. It truly was one of the marvels of the ancient world, and it's citizens were almost certainly sincerely altruistic in terms of prioritizing a greater good over themselves. And to be fair, most of the criticisms of it's structure are anachronistic; whether it was 'truly' egalitarian or very very limited egalitarian from a modern POV, compared with the vast majority of it's contemporaries it certainly was, and the other exceptions tended to rise/fall very quickly. In the Greek world they were viewed as an odd but successful experiment in something like socialism, or the Napoleonic Tri-colour egalite, fraternity but somewhat less liberte. So, admirable in a way.
It's just a terrifying model, but an extremely tantalizing one for political architects of a nationalistic/militaristic persuasion.
