Instead of delving into any Biblical exegesis involving passages that on the surface appear to say that God can/cannot change his mind, I want to think about some of the philosophical consequences of however one chooses to answer this question. Consider this argument:
1. It is a mark of human integrity to be able/willing to change one's mind. (Premise)
2. God cannot change his mind. (Premise)
3. Therefore, God does not exhibit the human element of integrity to change his mind. (From 1 and 2)
I fully endorse this argument. The problem is that I don't see how it does any damage to God's character. Of course God doesn't always exhibit the same virtues as humans in the same manner. Yet, that only raises an additional question: why should God have to be able/willing to change his mind in order to be maximally great? Think of it this way:
4. An omniscient mind, God, knows every propositional truth. (Definition)
5. Necessarily, if God knows every propositional truth, then God would never have to change his mind. (Premise)
6. Therefore, God never has to change his mind. (From 4 and 5)
Where, then, is the conflict between (3) and (6)? In fact, it would be a sign of weakness for God to change his mind when he already possesses all propositional knowledge!
Similar comments can be made about human nature exhibiting both actuality and potentiality. It is a sign of a human's virtue to actualize his or her potentiality. However, God qua pure actuality, has no need to actualize any potentiality, since he simply doesn't exhibit any potentiality.