About 10 miles slightly to the northeast of downtown Richmond,VA,the Battle Of Cold Harbor was fought on the dates listed in the title of this thread. Below is a link to the summary of the battle on the Civil War Trust website. It was a horrendous battle. It was the last battle fought between the Army Of Northern Virginia and Army Of The Potomac before both moved to Richmond/Petersburg and the long siege and series of battles that occurred there. You can find maps of the various stages of Cold Harbor at the CWT site too.
http://www.civilwar.org/battlefields/cold-harbor.html?tab=facts
http://www.civilwar.org/battlefields/cold-harbor.html?tab=facts