Every year, thousands of men (in 2007, over 40,000!) leave their families and travel to Rebbe Nachman's gravesite in Uman, a military city located in the Ukraine, to spend Rosh Hashana with "the Rebbe."
We pray much closer to home. I go with friends, just a mile or so from my house to Shiloh HaKeduma, Tel Shiloh every Rosh Chodesh to pray. In all honesty, I generally avoid praying at graves and tombs.
That's where the Mishkan, Holy Tabernacle rested (was located) for close to four hundred years, from when Joshua established Shiloh as the administrative and spiritual Capital of the Jewish People until Eli the High Priest's sons lost the Aron, Holy Ark in battle.
Eli was succeeded by Samuel the Prophet, the son of Chana (Hannah) who prayed for a son at Shiloh. She didn't want a son for personal, maternal reasons. She told G-d that she would raise that son to serve G-d and the Jewish People. It was Samuel who anointed the first two Jewish Kings, Saul and David.
The holiness of Shiloh remains to this day, and people of all religions come from all over the world to pray here. Archeologists and enthusiastic volunteers have been working hard to discover and uncover more of Ancient, Biblical Shiloh.
My friends and I generally come to pray on Rosh Chodesh, the first of the Jewish Month, but the next one is Rosh Hashanah, the beginning of the Jewish Year. So we'll join the big T'fillat Chana, Hannah's Prayer event being run by Shiloh HaKeduma on August 28. Contact Shiloh HaKeduma for more information about it. At present I only have a Hebrew poster to post here with information.