Much to the chagrin of Ancient Historians and Classicists, we only really have substantial evidence for two of the over 1,000 Greek poleis - Athens and Sparta. This is in no way down to the prominence of these two states, although they were prominent, but due to sheer accident. Athens had a remarkable literary tradition (and an epigraphical tradition seemingly unrivalled by anywhere else in Ancient Greece), birthing many great writers we associate with Ancient Greece, such as Thucydides or Xenophon, but there were many more writers from beyond Attica. Some of these we have, such as Herodotus of Miletus, but most we have lost, such as Hecataeus of Miletos or Hellanicus of Lesbos, and if these writers had survived in their entirety we would likely have a much greater understanding of Ancient Greece beyond Athens and Sparta. To really emphasise the relative dearth of evidence that has survived from Ancient Greece, Diogenes Laertius tells us that Aristotle's school produced works on the constitutions of 158 states (5.27), although these works would surely be somewhat flawed.

Of the two states we do know a substantial amount about - Athens and Sparta - only Athens is confidently reconstructed from our evidence, given, as I said, the literary and epigraphic material available to historians (there has been so much written about Athens that I won't really go into them). Sparta, on the otherhand, has no such comparable material. There are no surviving literary sources from Sparta, and the epigraphical record is somewhat sparse when compared to Athens. It is possible that Sparta did make significant use of inscriptions, but they may have utilised perishable materials with which to record them upon, such as bronze (see Millender, 2001 for a full discussion of Spartan literacy).

Moreover, what we do know about Sparta has come from non-Spartan writers, many of whom, if not all, were subject to the Spartan Mirage. The Spartan Mirage is "the ongoing tradition of idealized distortions and inventions regarding the character of Sparta in the works of non-Spartan writers in both Greek and Roman antiquity" (Hodkinson, 2002: viii), and this image is "what both Spartans and non-Spartans for various and often mutually inconsistent reasons wanted Sparta to be, to stand for, and to have accomplished" (Cartledge, 2002: 45). Thus, what is recorded about Sparta is dubious at best, and this is largely due to Athenian Laconophiles (Sparta-lovers) who saw Sparta as the ideal state to be emulated (see Aristophanes, Birds, 1281-4). Two of the most prominent surviving Laconophiles we have are Plato and Xenophon. Plato's Republic was likely modelled upon Sparta (Hooker, 1989: 136), while Xenophon's Lacedaemonian Constitution "dwells on, no doubt exaggerates, what was different, or unique, about life within Sparta" (Powell, 2018: 5). Additionally, despite warnings from throughout the 20th century about the reliability of the sources for Spartan history (see Starr, 1965), there was a tendency in scholarship, until the 1980s, to accept the literary testimony regarding Sparta uncritically, essentially accepting the belief that Sparta had an unchanging consitution (see Thuc. 1.18 and Cic. Flac. 63). As Flower (2002: 192) says:

"A traditional approach to the study of Sparta is to attempt to give a comprehensive description of the Spartan political, social, and educational instiutions during the 5th century BC, combining evidence from every period and from diverse authors, all of it taken more or less at face value. Alcman, Tyrtaeus, Herodotus, Xenophon, Polybius, and Plutarch are all treated as if they were contemporaries and their statements are accepted fairly uncritically and given equal weight."

So, much, if not all, of what we have concerning Sparta is subject to the Spartan Mirage, or even outright Spartan propaganda, such as the prominent myth of Spartan invincibility (see this answer by u/Iphikrates), and the resulting testimony was simply accepted by early scholarship. That said, since the 1980s Spartan studies have questioned the reliability of our sources, with Stephen Hodkinson spearheading this new school of thought. You won't go wrong with anything written by Stephen Hodkinson concerning Sparta, and I would recommend these pieces of his in particular to provide a good overview of Sparta (1, 2, 3, 4, 5). Our understanding of Helotage, Sparta's slave system, is also currently undergoing a significant change in scholarship, with an emphasis on Helots being chattel slaves under a different name, as opposed to the serf-like population favoured by earlier scholarship. David Lewis has provided an overview of the evidence for Helotage here (also see my previous answers: 1, 2, and 3). Additionally, Nino Luraghi (1, 2) and Hodkinson have both written on the functioning of Helotage, certainly a key aspect of the Spartan system to understand. If you can access it, I would suggest you check out Blackwell's A Companion to Sparta for an up-to-date overview of Spartan studies.

Another area of Ancient Greece that has an enigmatic position in Ancient Greek history is Crete. Similar to the Spartan Mirage, Crete is shrouded in a "fog of ancient misconception" (Whitley, 2009: 274), due to the ancient literary testimony treating the island as a monolithic political entity (see Perlman, 1992). The literary evidence, however, shouldn't be neglected (see Papakonstantinou, 2002). Much of the discussions concerning Crete surround the epigraphic legal evidence, since Crete has an abundance of inscriptions when compared to other regions of Ancient Greece, and if you can access it, I would suggest you check out Gagarin and Perlman's The Laws of Ancient Crete c.650-400 BCE for a comprehensive discussion of the evidence. I would also suggest Willets' The Civilisation of Ancient Crete, although be aware it is somewhat dated.

I would suggest that you also check out Hodkinson and Brock's Alternatives to Athens for a non-Athenocentric view of Greek poleis. The sources I have cited and links I have provided should give a good starting point to learning about relatively misunderstood Greek states.