Gibbon starts off chapter XXIII as follows:
The character of Apostate has injured the reputation of Julian; and the enthusiasm which clouded his virtues has exaggerated the real and apparent magnitude of his faults. Our partial ignorance may represent him as a philosophic monarch, who studied to protect, with an equal hand, the religious factions of the empire, and to allay the theological fever which had inflamed the minds of the people from the edicts of Diocletian to the exile of Athanasius. A more accurate view of the character and conduct of Julian will remove this favourable prepossession for a prince who did not escape the general contagion of the times.
Despite this disclaimer, I suspect most people who read Gibbon's account of Julian in chapters XIX and XXII to XXIV do come away with a "favourable prepossession for" Julian.
In his introduction to the first volume of the Penguin unabridged edition, which contains Gibbon's Volume the First and Volume the Second, David Womersley suggests that "Volume 2 can be seen as a diptych, although it is a nice question whether the portraits are paired or opposed. Chapters XVII to XXVI are in large measure devoted to the reigns of Constantine and Julian the Apostate, ..." (pg. xlii). He goes on to argue that although Gibbon started off with the view common in Enlightenment circles of Julian as a hero fighting against the stifling and corrupt power of the church, Gibbon came to a more ambivalent view of him as he studied him more -- hence the disclaimer above.
Gibbon's final words on Julian at the end of Chapter XXIV still show a certain prepossesion for him, despite the criticisms that precede them:
The remains of Julian were interred at Tarsus in Cilicia; but his stately tomb, which arose in that city on the banks of the cold and limpid Cydnus, was displeasing to the faithful friends who loved and revered the memory of that extraordinary man. The philosopher expressed a very reasonable wish that the disciple of Plato might have reposed amidst the groves of the Academy, while the soldier exclaimed, in bolder accents, that the ashes of Julian should have been mingled with those of Caesar, in the field of Mars, and among the ancient monuments of Roman virtue. The history of princes does not very frequently renew the example of a similar competition.
Two satires by Julian, Misopogon (the Beard Hater) and The Caesars (also known as Symposium or as Kronia) are both on line in translation. The University of Michigan has put this collection of Julian's letters on line (the actual letters start from page 36).
Most of the surviving part of Ammianus Marcellinus' work and, assuming the lost books are about the same size as the parts which have survived, probably about 1/3 of the total work, deals with Julian's time as Caesar and then Augustus. Ammianus provides an obituary notice of Julian summarising his character and his virtues and vices.
Favourable and unfavourable contemporary views of Julian can be seen in Libanius' letters to Julian and funeral oration and two invectives against Julian from Gregory Nazianzen, a Christian bishop.
For a modern view of Julian, see the DIR entry.