However, both queens took their own lives. Shouldn't they be placed in the seventh circle, with the other suicides?
Dante conceived of the architecture of Hell as an inverted church. The higher circles are lesser sins, and each descending circle represents what he saw as greater sins.
The sin of Lust was, to Dante, getting so swept up in your passion or your emotion that you lost sight of God. That was both Dido's and Cleopatra's besetting sin.
From John Ciardi's translation, p46:
[Dante and Virgil] find themselves on a dark ledge swept by a great whirlwind, which spins within it the souls of the CARNAL, those who betrayed reason to their appetites. Their sin was to abandon themselves to the tempest of their passions, so they are swept forever in the tempest of Hell, forever denied the light of reason and of God. Virgil identifies many among them. SEMIRAMIS is there, and DIDO, CLEOPATRA, HELEN, ACHILLES, PARIS, and TRISTAN.
The other is Dido, faithless to the ashes
of Sichaeus, she killed herself for love.
The next whom the eternal tempest lashes
is sense-drugged Cleopatra.
While suicide is an attack against God — wasting the life you were given — both women killed themselves out of grief over losing a man they loved (Aeneas and Mark Antony respectively). Both of them committed suicide out of Lust/love/passion, not out of depression or rejecting God. They would have been damned for their excess lust, in Dante's view, no matter how they died.
from p112, Circle Seven, Round Three:
...the Poets move on to the next round, a great PLAIN OF BURNING SAND upon which there descends an eternal slow RAIN OF FIRE.
On the edge of this plain is the Wood Of Suicides, but the text really doesn't give us much. There's a lot about the other kinds of sinners there, who are violent against God, Nature, and Art, but nothing really about the Wood itself. Virgil tells Dante (p115):
["]Now follow me; and mind for your own good
you do not step upon the burning sand,
but keep well back along the edge of the wood."
Dante's view of Hell is that each person chooses his or her own punishment in the way s/he actively chose to turn away from goodness and God in life. So Dido and Cleopatra chose to wallow in physical lust and then grief. Conversely, Capaneus died cursing God (actually cursing Jove, an interesting juxtaposition) while storming Thebes, so his sin was blasphemy, earning him a place in the seventh circle.