Never let team Black stans and Targ fanboys gaslight you to believe that house Hightower is an enemy of house Targaryen:
1) Before the conquest, Aegon and Visenya visited the Oldtown and were allowed to spend time at the Citadel.
2) The Hightowers did not march to the Field of Fire, and surrendered without a fight.
3) Aegon's reign officially began in Oldtown after he was anointed and crowned by the High Septon (who was a Hightower) in the Starry Sept, and was celebrated by the people as he rode over the city on Balerion.
4) House Hightower was one of the few houses that helped the Targaryens in the First Dornish War.
5) Aegon agreed to betroth his son Maegor to Ceryse Hightower when Ceryse's uncle suggested that Maegor should be wed to his niece. Look what F&B has to say about Maegor and Ceryse: "Maegor boasted to having consummated the marriage a dozen times the night of the wedding, and those who had seen the bedding agreed that Maegor was a lusty husband."
6) Maegor recognized Ceryse as the official Queen of Westeros, even though he had two more wives, and gave all of her lands and titles back to her.
7) When Rhaena Targaryen fled from Maegor, he sent a rider to Oldtown commanding Lord Hightower to behead Rhaella (who was training to become a Septa) as punishment for her mother's betrayal. Lord Hightower refused, and imprisoned the messenger instead.
8) Alicent fetched old Jaehaerys' meals, helped him wash and dress, and read to him. On her deathbed, she said: "I want to see my sons again, and Helaena, my sweet girl. Oh... and King Jaehaerys. I will read to him, as i did when i was little. He used to say i had a lovely voice." She didn't mention her father or her brothers, but she mentioned Jaehaerys. That shows how much she loved him.
9) Rhaena Targaryen (Daemon's daughter) married Garmund Hightower and had six daughters by him. As one of the few remaining heirs to the iron throne and the sister of the King, she had no reason to marry a third son and have not one, not two, but six daughters by him if she didn't love him.
10) They remained loyal to the Targaryens during the Robert's Rebellion.
11) Unlike Jaime Lannister and Barristan Selmy, Gerold Hightower remained loyal to Rhaegar till his last breath. He refused several opportunities to leave unharmed, and eventually died while defending Rhaegar's son.
12) Daenaerys thinks house Hightower is among the houses that will help her take back the iron throne. She assumes correctly because the Hightowers believe in a prophecy that says Oldtown would burn and its monuments would be cast down if they opposed the "Blood of the Dragon." That's why they gave full support to neither side during the First Blackfyre Rebellion, keeping a foot in both Targaryen and Blackfyre camps.