This is a harder question to answer than what's at face value. So I do apologize for this going longer than I expected.
The question: Does God change His mind?
First I want to clarify something. I believe that God knows everything. That He is outside of our limitation of time, and that everything He does has a purpose for His ultimate glory.
So, if you are asking if God changes His mind because of new information being presented to Him, then that is a big no. I do not believe He changes His mind. Yet...
There are Scriptures that show God changing His mind. The Jonah example is a good one. God did say He was going to destroy the Ninevites after forty days. He also sent a prophet to them, telling them of the destruction at hand. They heard the doom and gloom, repented, and God spared them in His grace.
Another good example is found in Exodus 32:14
"So the Lord changed his mind about the terrible disaster He had threatened to bring on his people."
Here, the Israelites made a calf idol and began worshipping it as the god that rescued them from Egypt. God tells Moses that He will wipe them out and start over with him. But Moses pleads for the people, and God, changes His mind...
The biggest issue with the thought that God changes His mind is the very fact that God knows all things. (1John 3:20) But as we see in Scripture, it would appear that He does... sort of.
Follow my logic here;
If God knows everything, then from an eternal perspective, God does not change His mind. He would already know the outcome before it began. Yet from our perspective, a temporal perspective, He does. Confused?
God never changes, (Malachi 3:6), and He said, “If that nation against which I have spoken turns from its evil, I will relent concerning the calamity I planned to bring on it,” (Jer. 18:8). So from this we can see that He didn't change His mind concerning Ninivah. He sent Jonah, knowing they would repent, and He would be able to show them His grace. Jonah even knew it and that's why he didn't want to go in the first place. (Jonah 4:2)
As for Moses pleading on the Israelites behalf. We often see God has a way of revealing things through, shall we say, procrastination. For example, Jesus is told Lazuras is sick. Jesus knows he is going to die, yet doesn't go anywhere. He waits for poor Lazuras to die before He goes. Why? So He can show God's glory.
Now, back to the Moses situation. God keeps him up on the mountain for forty days. You know that God knows the Israelites are going to sin by idolatry and if Moses had been allowed to go down, it would have prevented it. But He didn't. He let them have their way, so He could be angry, for Moses to intercede, so God can relent, and finally, so He can show His grace by changing His mind.
The Old Testemanent is full of God revealing Himself in types and symbols. These types and symbols point ahead to Jesus. Here, Moses as a type of Christ, is interceding on the behalf of his people.
So, in my humble opinion, what we see here is God changing His mind from our perspective, but not from an eternal perspective.
Thanks for reading the ramblings of a rambler,