There are, as far as I can discover, two monasteries claiming that name Carmelite that have the Traditional Latin Mass (leaving aside a few sedes/SSPX afiliated groups scattered around) - the Carmel of Jesus, Mary and Joseph, Nebraska, USA for women, and the Wyoming Carmelite monks. Both currently have an Australian in residence!
Origins of the Carmelites - a little history
The Carmelites trace their history back to Elijah and the community of hermits on Mt Carmel, but so far as historical records are concerned, their modern incarnation really starts with a group of Westerners who settled there during the Crusades. This group were strict hermits, and followed the Rule of St Albert. The collapse of the Crusader kingdoms forced them back to Europe, and once there, they quickly abandoned (or adapted depending on your perspective)their original charism and remodelled themselves on the mendicant orders, particularly the Dominicans, becoming friars rather than monks.
The nuns were founded in 1452 as part of a reform movement, and the third order in 1476, but the most famous reformer of the Order was of course St Teresa of Avila, aided by St John of the Cross, which saw the split off of the 'discalced' (no footwear, or sandals allowed for the friars) Carmelites, a much more ascetic group, in the sixteenth century.
As for virtually all religious orders, the Carmelites were almost wiped out in Europe by the French Revolution (made famous by the Dialogues of the Carmelites) and Napoleon - at the end of the nineteenth century there were only 200 Carmelite men left.
In the twentieth century, however, there has been something of a revival, helped greatly by the popularity of saints such as Therese of Lisieux.
The Carmelites are a very strict, penitential order, with a hermetical orientation - I've seen them described as 'hermits in community'. The traditional women's Carmel practices very strict enclosure, in keeping with St Teresa's view that this was necessary to achieve the heights of contemplative prayer. St Teresa, in fact, didn't want to have laypeople formally associated with the Order; that was a much later innovation.
They particularly differ from Benedictines in that private prayer rather than liturgy is their main focus - they sing the Divine Office on one note (recto tono) rather than chant for example. And they differ from both Benedictines and Dominicans in not making study a major emphasis, as the story of St Therese of Lisieux not even having a Bible illustrates (while her contemporaries, founding the Benedictine women's house at Solesmes not only each had their own Bible, but were learning Latin and patristics - of course, St Therese is the one who has been named a Doctor of the Church)!
The Carmel of Jesus, Joseph and Mary
The traditional women's Carmel was dedicated in 2000 - prior to that the sisters lived in a farmhouse nearby, but there is surprisingly little about there history on the net. They are now pretty close to full, with 21 nuns (though some are still in formation) so are looking at making a new foundation (but I don't know where this is up to...anyone know anything?).
The Wyoming monks
The monks are, as far as I can gather, a return to the older form of Carmelite life for men, in that, unlike the friars, they are strictly enclosed (while following Teresian spirituality). They started in 2003, and have 8 monks, plus another large group in various stages of formation.
So go and take a look at their website - it is really excellent.