Prince Daemon Targaryen's wife is Lady Rhea of one of the oldest Houses in the realm, House Royce.
Very little is known of Lady Rhea at this point, but I thought it best to highlight something especially for show-only folks -- When Otto Hightower brought up Daemon Targaryen's wife as a way to needle him, Daemon was dismissive of her. The comment about her looks, and the looks of women in the Vale in general, was rather cruel. The marriage was clearly not a love match, but why would a Targaryen prince like Daemon be married to a daughter of a House that has been mentioned (the very first lord we saw in Game of Thrones was a Royce, Waymar, one of the rangers who went beyond the Wall) but has not really been that prominent compared to Houses like Stark, Lannister, Tyrell, and Martell?
First off, Daemon was married in 97 AC during the reign of his grandparents, King Jaehaerys and Queen Alysanne, a time when there were plenty of Targaryens about. There is no mention so far in the texts (at least, the ones I've read) on why Daemon was married to a member of House Royce; my guess is, this is a political match, perhaps one arranged by his grandmother the Queen. House Royce is one of the most ancient Houses in the Seven Kingdoms. The Royces descended from the First Men (like the Starks) and called themselves Bronze Kings. During the Andal Invasion and the subsequent wars that lasted generations between the First Men and the Andals, the Bronze Kings led the resistance and had several notable victories. Still, the Andals pressed on, and eventually, they controlled three-quarters of the Vale. The last Bronze King, Robar II, persuaded the First Men who were left resisting the Andal advance to unite, some of them petty kings themselves; they bent the knee and proclaimed him High King of the Vale, the Fingers, and the Mountains of the Moon. After King Robar was slain in the Battle of the Seven Stars, Artys Arryn was named King of Mountain and Vale. Thousands of years later, the Arryns still held the Vale.
In a world where an ancient name was valued, the Royces were very high up in terms of prestige. Marriage to a Royce provided the Targaryens, a relatively new name in Westeros, a link to one of the most ancient lineages in the Seven Kingdoms. Daemon's wife, Lady Rhea Royce, was heir to Runestone, the ancient seat of House Royce. Since there was no expectation at that time that Daemon would be close to kingship, marriage to Lady Rhea provided him with a suitable seat.
The Royces were also bannermen to the Arryns, who had strong links to the Targaryens. Lord Rodrick Arryn served as lord justiciar and master of laws on the Small Council at the time of King Jaehaerys. When the despairing King and the dutiful Queen Alysanne made their gentle and rather simple daughter Princess Daella choose a husband, she chose Lord Rodrick, and for a time she lived happily in the Eyrie, until she passed away after giving birth to her daughter Aemma. Aemma Arryn would later marry Viserys Targaryen. When Viserys became King, Daemon asked his brother to set aside his marriage to Lady Rhea. Viserys denied this request.
In the Game of Thrones years, the head of House Royce was Yohn Royce, also known as Bronze Yohn. Young Lord Robert Arryn of the Vale (Robin Arryn or Sweetrobin) was left in his care in the fifth season, a testament to the continued power and prestige of his House. One of my favourite things about House of the Dragon is how we get to see and learn more of these fascinating Houses. Is it possible that we may see Runestone at some point? Well, I'd like to see every location there is, so, hopefully! Within the Vale, however, the Eyrie would be the more likely bet.