Erzurum is the highest major city (population: 360,000 according to 2000 census) in Turkey, situated at an altitude of about 2000 metres over the sea level. Complemented with the distance to the sea, this makes the climate of this area the harshest in Turkey with the temperatures in long, heavily snowy, and bitterly cold winter regularly below -30°C at nights (and no warmer than -15°C during the day). Wet summers in Erzurum are around 30°C in the day time and is chilly at night time, although temperatures dropping down to freezing point during summer are becoming rarer and rarer each year, probably with the advance of the global warming.
The city hosted the international 2011 Winter Universiade (“university olympic games”) .
There is a daily train from Istanbul (Doğu Express, departs from Haydarpaşa station at 08:35 every morning). Doğu Express has a stop in Ankara, too (and in a number of other cities and towns across Anatolia, including Eskişehir, Kayseri, Sivas, and Erzincan among others as well). There is also another daily train from Ankara (Erzurum Express, which is said to be more comfortable than Doğu Express). Both trains head for Kars — further east (near Armenian and Georgian borders). See Turkish Republic State Railways website for schedules and fares: 
Most bus companies stop at the Erzurum Otogar, which is about 1 km away from the main city centre. It is a walkable distance to town, or you can take the public bus to/from the Otogar.
Buses from Trabzon are available (4.5hrs and 30LT, 25 if you don’t look like a tourist and don’t speak much english) .
Erzurum is a pretty small city, and you can cover most of it by foot, unless you are thinking of heading out and around the city, in which case, most public buses and taxis will be able to get you there.
Citadel of Erzurum - The Citadel of Erzurum is situated on the top of the hill in the middle of the city centre. The YTL 3 admission fee allows you to explore the grounds as well as to climb up the minaret/clock tower, as well as visit the citadel masjid. It's worth the effort to climb up the clock tower as it gives you a commanding view of the city as well as the surrounding mountains.
Stockbreeding is widespread in the region, and there is little chance to cultivate vegetables and fruits in this high and cold land. Therefore traditional food is mainly dependent on meat.
The city is also known for different types of local cheese that is hard to find elsewhere in Turkey.
Kadayıf dolması — A must-taste local dessert of Erzurum cuisine. It is made from kadayıf, a sweet pastry that is lots of thin fibres of flour put together. Walnuts are stuffed in the kadayıf and the stuffed kadayıf is first fried, then cooled and finally ready to serve with addition of a sweet sauce. It may be sampled in virtually every restaurant in Erzurum, but some of the best can be tried in a specialist restaurant, Muammer Usta 
Döner — Typical Turkish döner is really made well and should be tasted in Hacı Baba Restaurant  on Emniyet Caddesi.
Cağ kebap — local kebab of Erzurum, that you can have in Gelgor Restaurant. It is made with lamb meat and the preperation is like döner, but unlike döner, instead of a vertical axis, the meat is cooked on a horizontal axis.
Güzelyurt Restaurant — A very nice old restaurant right in the city center on Cumhuriyet Caddesi. You can have a good Turkish meal with some Turkish raki and enjoy the atmosphere. 
Hmmburger — A very tiny small hamburger place. Hamburgers are really delicious.
Coffeebox — A local coffeeshop, with various pasta options and nice coffees.
The area code of Erzurum is 442. Dial +90 442 when calling from out of Turkey.