In Shakespeare's As You Like It, Duke Frederick exiles his niece Rosalind from his court. Rosalind's cousin Celia decides that they should go to the forest where Rosalind's father, Duke Senior, has been banished.
ROSALIND. Why, whither shall we go?
CELIA. To seek my uncle in the forest of Arden.
ROSALIND. Alas! what danger will it be to us,
Maids as we are, to travel forth so far?
Beauty provoketh thieves sooner than gold. (1.3.85–89)
According to Rosalind, the Forest of Arden can be a dangerous place, so Celia decides to dress like a shepherdess, "in mean attire," and Rosaline chooses to dress herself in "all points like a man," to avoid any thieves who might be provoked by their beauty.
In A Midsummer Night's Dream, Hermia's father, Egeus, forbids her to marry Lysander and demands that she marry Demetrius. Theseus, Duke of Athens, agrees with Hermia's father and orders Hermia to marry Demetrius, be put to death, or join a convent.
Hermia doesn't like any of those options and instead conspires with Lysander to run away to his aunt's home, about twenty-four miles from Athens, where they can be married, away her father's influence and outside the Duke's jurisdiction.
Lysander and Hermia agree to meet the next night in the woods about three miles outside Athens and to proceed from there to Lysander's aunt's home.
LYSANDER. ...[T]herefore, hear me, Hermia.
I have a widow aunt, a dowager
Of great revenue, and she hath no child:
From Athens is her house remote seven leagues;
And she respects me as her only son.
There, gentle Hermia, may I marry thee;
And to that place the sharp Athenian law
Cannot pursue us. If thou lovest me then,
Steal forth thy father's house tomorrow night;
And in the wood, a league without the town,
Where I did meet thee once with Helena
To do observance to a morn of May,
There will I stay for thee. (1.1.158–170)
Lysander doesn't mention any "dangers" in the woods or anything about maids provoking thieves, and he doesn't suggest that Hermia dress like a man.
Later in the play, Oberon, King of the Fairies, describes an idyllic place in the woods where Titania, Queen of the Fairies, likes to sleep.
OBERON. ... I know a bank where the wild thyme blows,
Where oxlips and the nodding violet grows,
Quite over-canopied with luscious woodbine,
With sweet musk-roses, and with eglantine;
There sleeps Titania sometime of the night,
Lull'd in these flowers with dances and delight... (2.1.254–259)
There are no dangers lurking in the woods outside Athens in A Midsummer Night's Dream, and there are no thieves provoked by beauty that Lysander and Hermia might encounter. There are only mixed-up lovers (Lysander, Hermia, Demetrius, and Helena), a considerable number of fairies, a man with the head of an ass, and some local townsfolk, whom Puck calls "a crew of patches, rude mechanicals" (3.2.10), rehearsing a play that they intend to perform at the Duke's wedding.
In time, Rosalind and Celia find the Forest of Arden in As You Like It a suitably hospitable and even pleasant place, populated not by beauty-provoked thieves but by gentle, if sometimes not too bright, country folk (Phoebe, Silvius, Corin, Audrey, and William), as well as displaced and confused city folk (Orlando and Oliver), some of whom fall in love with Rosalind (Orlando and Phoebe) and Celia (Oliver).
Oddly, even though Lysander and Hermia leave Athens forever to live with Lysander's aunt twenty-four miles away, neither of them carries any luggage. Neither do Rosalind and Celia, who appear in women's clothes (if not wedding clothes) when they marry Orlando and Oliver, respectively, in the last scene of the play. Perhaps Lysander and Hermia had their luggage sent ahead to Lysander's aunt's place, and Rosalind and Celia stored their personal trousseaux in hollowed-out trees while they wandered in the forest.
Nevertheless, everyone lives happily ever after—not in the Forest of Arden or the woods outside Athens, but back in their respective cities. Apparently the woods are a nice place to visit and offer a welcome respite from the trials and tribulations of city life, but none of the visitors choose to live there.