Along with Satan, Eve is the most important character in Paradise Lost; it is her idea to separate from Adam (in Book 9), and she is the one who first eats the Forbidden Fruit and then convinces Adam to eat it. In many respects, then, Eve's not likeable from the get-go. And in other respects, she's totally likeable for her sense of independence and curiosity. After the Fall, Adam and Eve engage in a petty blame game, where it becomes clear that, yes, Eve ate first, but Adam also ate the fruit, for his own reasons (chiefly because he didn't want Eve to go down alone).
OK, so Eve seems to be a bit of a rebel. Granted, the first thing she does upon coming to life is stare at herself in a lake (4.460) like Narcissus – a mythological figure who fell in love with his own reflection and died as a result – until God leads her away. In Book 9, she is called "our credulous mother" (9.644), an ominous name because we learn that Satan's words "too easy entrance found" (9.734) their way into her heart. Then there's all the stuff about how Adam is somehow more perfect because he was created first (Eve was made out of his rib) and resembles God more than she does (see 10.150-151 for one example of this idea). And of course, who can forget our very first encounter with Eve in Book 4, where Milton writes that "both/ Not equal, as their sex not equal seemed" (4.295-296). Huh?
But wait, the word "seemed" suggests that this is someone's point of view rather than cold hard fact (things "seem" to somebody). In this case that observer is…Satan! Yes that's right, our first glimpse of the primal couple (and of a potential inequality in the sexes) is through Satan's eyes. In that sense, the passages surrounding line 295 in Book 4 make it seem as though only Satan, or someone like him, would think that men and women aren't equals.
Now, we don't mean to suggest that Milton is some kind of early feminist (he definitely is not that). We only mean that Eve is a tougher nut to crack. So, for example, the narcissism scene is, in reality, pretty innocent. Imagine if you didn't exist and then all of a sudden you did. What would you think of your own face? Or imagine if you grew up without any means of looking at yourself or seeing your reflection, and then, one day, you found a mirror. You would be fascinated because you wouldn't recognize it as your own face! You've never even seen it! Ditto Book 9; it's hard to blame Eve and act as if Adam wouldn't have done the same thing if he were in the same situation. We're not sure if Adam would have been able to resist Satan – he can't even resist his wife, let alone the most rhetorically gifted speaker in English literature.
The thing to keep in mind then is that Eve isn't always as bad or stupid as she seems or as she is portrayed. Sometimes people like to complain that Eve is left out or excluded from the boys' club; for example, when Michael comes down to give Adam his little history lesson in Books 11 and 12, Eve is put to sleep. When Raphael and Adam have their little conversation, Eve doesn't really participate; eventually she gets up and leaves. But the reason she gets up and leaves (at the beginning of Book 8) is not because she can't handle the dense, theoretical conversation about the origin and structure of the universe (something that is too obscure or highfalutin for most contemporary readers). She gets up because she would rather hear her sweetie narrate it. Eve is just as capable as Adam of having serious, scientific conversations; she just wants her husband to interpose little kisses and caresses while they talk. Wouldn't you? It's a kind of touching scene.
The fact of the matter is that Eve is innocent and well-meaning, except for that little slip up with the fruit. We probably aren't supposed to read the narcissism scene, or the evil dream that Satan whispers in her ear (recounted near the beginning of Book 5), or even her suggestion that she and Adam divide their labor so they can actually be productive (beginning of Book 9), as somehow foreshadowing the huge mistake she eventually makes. Milton very much wants to create the impression that the Fall hasn't happened yet and that things might go the other way. God says on numerous occasions that Adam and Eve weren't fated to do anything, and that he gave them free will. So, just because Eve's hair is described as "wanton" (4.306), for example, a word with more negative connotations than positive ones, doesn't mean she is somehow "bad" from the get-go. We always have to remember that we are seeing Eve through someone else's eyes.