I'd recommend picking up a copy of Carthage Must be Destroyed by Richard Miles. I believe he has somewhat of a discussion of Hannibal's character.

Unfortunately there are very very few sources on what Hannibal was actually like. Livy paints a portrait of him early in The War with Hannibal (which can be accessed for free online) which praises and condemns Hannibal, but of course its a very biased source.

There are a few stories about Hannibal which might say something about his character. After Carthage's defeat at the battle of Zama the Carthaginian Senate was discussing what course of action to take. One man got up to speak in favour of continuing the war but was dragged offstage by Hannibal, who later apologised for doing so. One might infer that Hannibal was prone to emotional outbursts but I think the fact that he had been in command of an army for the last two decades meant that he was unused to the formality of the senate house. Certainly, he would have been used to giving commands and having them obeyed.

Livy mentions that after each battle Hannibal searched for the body of the Roman generals and sought to give them a proper burial. He also released all Italians (but not Romans) who were captured by him. This suggests that Hannibal preferred to be generous. However, he could also be ruthless. After Cannae a group of Romans surrendered to Mago (one of Hannibal's officers) after he promised to release them with one garnment each. Hannibal, who had not given Mago permission to make such an offer, was determined to prevent Rome from recovering any manpower and threw them in chains. He offered to allow Rome to ransom all their prisoners, though this was probably because he needed more money.

After the Second Punic War Hannibal proved to be as capable a politician as he was a general. He reformed the Carthaginian government and made it so efficient that Carthage was in a position to pay off its massive war debt to Rome early. However, Hannibal quickly and suddenly fled Carthage when he realised he was in danger.

Clearly, Hannibal was extremely intelligent, capable of taking bold, decisive action as well as patient (as evidenced by his long years in Italy). He does not seem to have enjoyed violence and treated others with respect. He was brave (he fought in the front line at Cannae). Perhaps the most remarkable thing about Hannibal is his amazing capacity for leadership; he maintained an army on enemy soil for over a decade and engaged in constant hostilities without being defeated despite the fact that his army was made up of many different nationalities who spoke many different languages, and not once does there appear to have been any kind of mutiny or serious dissent. His tactical wit surpassed that of any other ancient general. Particularly his use of ambuscades (Trasimene), but also in open battle (Cannae).

One last story. Many, many years after the Punic war Hannibal and Scipio Africanus (supposedly, this was recorded by Livy in 'Rome and the Mediterranean') met in Turkey. Scipio asked Hannibal who he considered to be the top three generals of all time (hoping that Hannibal would name him - Scipio). Hannibal responded first Alexander the Great. Scipio was alright with this, since he too considered Alexander the best. Second, Hannibal named Pyrrhus of Epirus. Scipio grudgingly accepted this, since Pyrrhus was a fine general. Third, Hannibal named himself - Hannibal. Scipio, stung, laughed and asked Hannibal where he would place himself if Scipio had not defeated him. Hannibal replied that if he had not lost to Scipio, he would have placed himself first, thereby flattering Scipio by suggesting he had conquered someone who would otherwise have been better than Alexander.

SOURCE: Livy, the War with Hannibal. Livy, Rome and the Mediterranean.