Most of the civil war battles fought in Georgia took place in what year?

There weren't many major battles in Georgia.

In Summer '63, the Tennessee campaign briefly strayed over the Georgia line, with the battle of Chickamauga.

After Grant took charge in March '64, Sherman pursued Joe Johnston, who denied him any big actions (except Kennesaw), and then surrounded the city of Atlanta, but the Army of Tennessee escaped into the mountains.

Sherman then planned his March to the Sea - a campaign that got him identified with great brutality, though the bottom line is that he shortened the war by many months at almost nil casualties.

When he reached Savannah, everyone thought there would be a big destructive battle in that lovely port-city, but the small Confederate army got out into South Carolina, where Sherman would follow them in a few weeks.

Georgia had suffered much damage, but not many battles costly in lives.