It seems from the perspective of the Maesters that Jaehaerys started out a great guy and this was furthered by his wife and council.
Though young to the throne, Jaehaerys revealed himself from an early age to be a true king. He was a fine warrior, skilled with lance and bow, and a gifted horseman. He was a dragonrider as well, riding upon Vermithor—a great beast of bronze and tan who was the largest of the living dragons after Balerion and Vhagar. Decisive in thought and deed, Jaehaerys was wise beyond his years, always seeking the most peaceable ends.
His queen, Alysanne, was also well loved throughout the realm, being both beautiful and high-spirited, as well as charming and keenly intelligent. Some said that she ruled the realm as much as the king did, and there was some truth to that. It was at her behest that King Jaehaerys at last forbade the right of the First Night, despite the many lords who jealously guarded it.
With Barth's aid and advice, King Jaehaerys did more to reform the realm than any other king who lived before or after. Where his grandsire, King Aegon, had left the laws of the Seven Kingdoms to the vagaries of local tradition and custom, Jaehaerys created the first unified code, so that from the North to the Dornish Marches, the realm shared a single rule of law. Great works to improve King's Landing were also implemented—drains and sewers and wells, especially, for Barth believed that fresh water and the flushing away of offal and waste were important to a city's health. Furthermore, the Conciliator began the construction of the great network of roads that would one day join King's Landing to the Reach, the stormlands, the westerlands, the riverlands, and even the North—understanding that to knit together the realm it must be easier to travel among its regions. The kingsroad was the greatest of these roads, reaching hundreds of leagues to Castle Black and the Wall.
So it was quite natural for Jaehaerys to go down in history as one of the greatest if not the greatest of the Targaryen kings.
King Jaehaerys, the First of His Name—known as the Conciliator, and the Old King (being the only Targaryen ruler who lived to such an advanced age)—died peacefully in his bed in 103 AC, while Lady Alicent read to him from his friend Barth's Unnatural History. He was nine-and-sixty at his death, and had ruled wisely and well for five-and-fifty years. Westeros mourned, and it was claimed that even in Dorne men wept and women tore their garments in lament for a king who had been so just and good. His ashes were interred with that of his beloved, the Good Queen Alysanne, beneath the Red Keep. And the realm never saw their like again.
All above quotes from The World of Ice and Fire - The Targaryen Kings: Jaehaerys I
So how much of this can be credited to Jaehaerys himself or to his council? It was all teamwork among those who loved each other and were friends. However, in the end the king has the final say and his own tendencies (good or bad) would ultimately shine through.