How good a statesman was Hannibal?

Secondary historians

In the past, it was common for historians to regard Hannibal as a great statesman, as well as a great general:
• The American Colonel Theodore Dodge concluded (1895) that 'Hannibal was equal as a statesmen to what he was as a soldier'
• The British historian William O'Connor Morris claimed that 'Hannibal was an illustrious statesman'
• The German apologist Edmund Groag defended him against what he saw as the biased statements of antiquity, and represented Hanninal as a champion of the oppressed.

More modern historians, however, have tended to be more critical of Hannibal's diplomatic and political skills, and Michael Fronda (2010) regards Hannibal's failure to organise the Italian League as the cause of his strategic failure and the loss of the war.

Contemporary Writers

Modern Historians disagree about the validity of the extant record - some regarding it as so biased and fictional as to be virtually worthless, with others seeing it as more-or-less a true record from the Roman's-point-of-view.

Polybius was generally dismissive of Hannibal's diplomatic skills - when the Roman ambassadors come to protest about the attack on Saguntum: 

Polybius, Book 1, Chapter 3
Hannibal, being young, full of martial ardour, encouraged by the success of his enterprises, and spurred on by his long-standing enmity to Rome, in his answer to the legates affected to be guarding the interests of the Saguntines and accused the Romans of having a short time previously, when there was a party quarrel at Saguntum and they were called in to arbitrate, unjustly put to death some of the leading men. The Carthaginians, he said, would not overlook this violation of good faith for it was from of old the principle of Carthage never to neglect the cause of the victims of injustice... 
Being wholly under the influence of unreasoning and violent anger, he did not allege the true reasons, but took refuge in groundless pretexts, as men are wont to do who disregard duty because they are prepossessed by passion …

Where he records them at all, Polybius generally records Hannibal's diplomatic successes as 'just happening', and at Nagarraga he portrays a man 'begging' for his country's safety ... and then suggesting totally unreasonable, too-lenient terms.

Livy is actually hostile. Where he succeeds, Hannibal uses bribery or force; and in his negotiations with Philip of Macedon and Scipio, he is portrayed as a pantomime villain.  Throughout, Hannibal is represented as exhibiting the 'Punic treachery' of his race. 
Only in one matter does Hannibal appear favourably in Livy - he is seen as a reformer, attempting to reform the 'despotism' and corruption of the Carthaginian government... until he fails and flees into exile.

You be the Judge

This is a matter on which you can make your own judgement.

Consider this list of diplomatic/political actions by Hannibal:

1   He rejected the Roman ambassadors who came to ask him to raise the siege of Saguntum

2   He organised his support in Carthage to ensure he was supported, despite Hanno's opposition

3   He made alliances with the Gauls before setting off from Spain

4   [Livy only] he negotiated successfuly at Iliberi with the tribes of the Pyrenees

 5   He made arrangements with the tribes of southern France

6   He formed an alliance with Magilus and the Boii before he crossed the Alps

7   He was invited to adjudicate between the [Allobrigian?] brothers, and formed an alliance

8   He saw through the false alliance offered by an Alpine tribe

9   Once in Italy, he secured alliances with the Cisalpine Gauls by a mixture of terror, leniency, military success, and posing as a liberator

10 After Cannae, he formed an Italian League with a number of southern Italian cities,including

11 An alliance with Capua

12 [Livy only] he maintained his support in the Carthaginian government, so that they continued to support him and send reinforcements

13 He made an treaty of friendship with Philip of Macedon
14 He asked for a Conference with Scipio, although he failed to negotiate a peace deal

15 He was reprimanded for using violence against one of the Mighty Ones

16 After the Peace Treaty, he became Suffete in Carthage and set about reforming the government and making it more democratic.