Minibuses to Dogubeyazit and Yuksekova for border crossings to Iran.
There are also two buses a day to and from Urmia in Iran costing only 15 Euros.
From Istanbul’s Haydarpaşa station (on the Asian side) there are trains direct to Tatvan, a town on the west side of Lake Van, three times a week. This train (Vangölü Express) departs Haydarpaşa on 20:05 (08:05 pm) and calls in a number of cities and towns across Anatolia, including Eskişehir, Ankara, Kayseri, Sivas, and Malatya among others. According to the timetable all the way between Istanbul and Tatvan takes almost 42 hours, frequent and probably long delays discluded. This is the longest (both in terms of miles traveled and time spent inside the train) non-international train journey in Turkey and gives a through panorama of almost all regions of inland Turkey. Inter Rail pass is accepted in this train. Once arrived in Tatvan, you can take the ferry which crosses the lake to Van.
Apart from Trans-Asia, there is also another international train service once a week (one of the days which Trans-Asia doesn’t call) between Van station and Tabriz in NW Iran.
There is a ferry line in the Lake Van, between Tatvan on the western shoreline and Van on the eastern shoreline.
The city is famous for its breakfast halls (kahvaltı salonu), in which for a not-so-high price, you are served a really filling breakfast including locally produced cheese (different types) and honey among many other stuff. The price usually includes an unlimited amount of tea. Look around.
Iran is only tens of kilometres away in the east. It is possible to go by road or rail. (Be sure to have your visa before you arrive in Van)