David's flight from Shaul, according to Sefer Shmuel (Alef chapter 19 - Bet chapter 2). David starts in Beit Lechem (his family home), and finishes in Hevron, after Shaul has died and he has become king.
Some speculative place identifications are based on shiurim from R' Yaakov Medan. Original map is from Koren Tanach.
Here is what David did in each place:
Ramah, Nayot be-Ramah - chased by Shaul
Givah - meets Yonatan, who shoots arrows as a signal
Nov - hides, city later massacred by Shaul
Gat - pretends to be insane, leaves
Adulam cave - hides, collects fellow rebels
Mitzpeh Moav - stays under Moav's protection
Forest of Heret - returns from Moav
Keilah - defeats Philistines, then chased away by Shaul
Zif, Maon - chased by Shaul
Ein Gedi - hides with his men
Midbar Paran - hides with his men. Sends messengers to Naval who refuses to help. Marries Avigail when Naval dies.
Givat Hahachila - penetrates Shaul's camp at night
Gat - stays with Philistines, fights Amalekites, is given Tziklag by Philistines
Afek - joins Philistine camp going to fight Israel in Yizrael, but they doubt his loyalty and send him home
Tziklag - city sacked by Amalekites, David avenges it
Hevron - Philistines have killed Shaul so David returns to Israel and becomes king