Where were the first Crusade battles fought?
Ashkelon
During the Crusades, Ashkelon (known to the Crusaders as "Ascalon") was an important city due to its location near the coast and between the Crusader States and Egypt. In 1099, shortly after the Siege of Jerusalem (1099), an Egyptian Fatimid army that had been sent to relieve Jerusalem was defeated by a Crusader force at the Battle of Ascalon. The city itself was not captured by the Crusaders because of internal disputes among their leaders. This battle is widely considered to have signified the end of the First Crusade. Until 1153, the Fatimids were able to launch raids into the Kingdom of Jerusalem from Ashkelon, which meant that the southern border of the Crusader States was constantly unstable. In response to these incursions into Outremer, King Fulk of Jerusalem constructed a number of Christian settlements around the city during the 1130s, in order to neutralise the threat of the Muslim garrison. In 1148, during the Second Crusade, the city was unsuccessfully besieged for eight days by a small Crusader army that was not fully supported by the Crusader States.
First Crusade
The Princes' Crusade, by contrast, was a well-organized military campaign, starting out in late summer of 1096 and arriving at Constantinople between November 1096 and April 1097. 
The crusaders marched into Anatolia, capturing Nicaea in June 1097 and Antioch in June 1098. They arrived at Jerusalem in June 1099 and took the city by assault on 7 July 1099, massacring the defenders. A brief attempt by the Saracens to recapture Jerusalem was repulsed at the Battle of Ascalon.