Iraq, Iran, Armenia are the neighbors and that is making Eastern Turkey more interesting in present location and past stories. Some best to visit on a tour would be: the largest lake in Turkey, Lake Van is there. Old stager cheese of Kars and Kars Gruyere, Amazing Armenian Church of Akdamar, Urartian Castle from 9th Century BC with very proper walls; Ani Ruins and Mt. Ararat are all sites to take you towards the unread eras to the history.
Best time to visit would be little after the first week of April if you are visiting Kars, especially as sometimes the snow is pretty late and the temperature here in winter is mostly below zero.
Due to long distances of travel, if you are self-driving in the country; give a minimum ten days to explore this area as distances are long in between both cities of interest in the area and the country from west to east.
Except for Mt. Ararat, there are no official permissions requirements or safety issues except for the updated travel warnings of most consulates.
Unlike most of the neighborhoods of western countries, Eastern Turkey is an unlimited, vast, mountainous zone with full of history and it is the best location to enjoy watching the stars where all began.
It is easier to get to one of the cities from Istanbul now with direct flights and then city centers are about one hour drive away from airports most of the time. Our private tours are well-designed for that region, too accompanied by specific guides for different interests.