There are trains three times a week from Istanbul (Güney Express) via Ankara and a number of other cities on the way, including Kayseri, Sivas, and Malatya among others. There is also another daily train from Ankara (4 Eylül Mavi Treni), which takes the same route with Güney Express. On its way back to Istanbul, Güney Express, which comes from Kurtalan and Batman about 2 hours further east from Diyarbakır, departs from Diyarbakır on Mondays, Wednesdays, and Fridays around noon. Trains to Istanbul get really overcrowded during early August because of huge numbers of seasonal workers taking the train to get to hazelnut orchards around Adapazarı and Eastern Marmara on the way (short of two hours from Istanbul—the last stop of the trains), and it is impossible to find a ticket during that season without booking/buying the ticket in advance. Even if you can find a ticket, the ride is very uncomfortable, and because of the huge numbers of passengers getting off the train in almost each stop—even if it is in the middle of nowhere, where normally no one ever gets on or off—to replenish their water from station fountains, trains are extremely delayed, and it takes almost two full days to get to Istanbul. Avoid if you are not deadly on budget.
Many local bus companies offer services from cities all over Turkey. The bus from Erzurum takes 6 hrs (from 50TL tourist price to 35TL). The main bus station (otogar) is about 10 km away from city centre, along the highway to Urfa.
When traveling from Diyarbakir to west by bus be prepared for several ID check ups at military checkpoints.
The old city containing many mosques and churches, is a little run down but enclosed in antique walls. The city walls are very old and certainly worth a walk around. Some of towers are restored by the municipality and are easy to reach from the center of the old city. One such is Kechi Burcu, which offers a nice view of Tigris river below the city, and a great look over the city walls—a teahouse offering traditional tea is nearby as well. However, be careful while walking on the walls and do not enter into all of the towers which looks fancy enough, as some of them are home to junkies.
The old city is like a village in the middle of the city with village mentality; goose running around, women having cay in front of their houses and kids (who'll beg for money) shouting to foreigners the few English words they know. However, walking around in the city center is unique and totally different from other Turkish cities. You'll see people as they live their everyday kurdish life. If you are lucky, you may even get invited for a tea by a friendly shopowner.
To avoid problems, dress modestly. There is an extensive development outside including a pleasant park. It's called Gazi Kösk and it contains many teahouses and traditional bed-like constructions, where you sink into cushions and drink tea while overlooking the Dicle river below.
You can go for a walk on the old city wall. Get onto it at the northern gate and walk anticlockwise to Mardin Gate. Great views of the surrounding area and the city and it's free. Single tourists might be conspicuous, however, and should beware of pickpockets.
Many tourists only visit the old part of Diyarbakir, but don't miss the totally new and modern New City. Around Ofis district you find a lot of nice bars and cafès filled with lots of students and young couples. Some Bars have livemusic, but better ask some locals on the street for that. Don't worry about security issues as this part of the city is filled with policemen.
In the old city you will find many people manufacturing metal tools by hand - sickles, hammers, and other, mostly agricultural implements.
You can also find cheap (around 25 TL) traditional kurdish trousers, that older men wear everyday. Enjoy tea + bargaining sessions with some friendly Bazaar shopkeepers.
A must try is seropeh (ser û pê) which is a traditional kurdish stew made from the head and feet of a sheep. Very cheap and tasty. Restaurants serving this dish are very common in Diyarbakir, just look for lamb skulls displayed in the window.
The grill of lamb liver, ciğer kebabı, is a famous part of Diyarbakır cuisine.
Ekşili etli dolma, meftune, içli köfte are some other "must taste"s.
A mixture of wheat grain, chick-peas, and yoghurt called mehir is purpoted to be very good for stomach and is said to help healing stomach problems.
Diyarbakır is very famous with its desserts. Kadayıf, künefe are the two main types of desserts. They are acquired tastes, though, as they are very sweet and contain huge amounts of sugar. Saim Usta is perhaps the best place to have kadayıf in town, while for künefe, you should check out Levent Usta.
There are many teagardens in Ofis and along the Basalt city walls, where you can meet locals. People in Diyarbakir are very open towards foreigners and you'll have a hard time paying for your own tea.
There are many clean and reasonably comfortable hotels with air con, etc. around Inönü street, in the nordern part of the old city. Doubles for 40TL and cheaper available. Cheap options are also available around Dagkapi square if you want to avoid dodgy areas at night but still within the old wall.
One cheap option is Divan Otel at Gazi Cad. # 9.
Diyarbakır is rough. At first glance, it seems not a very welcoming city, actually it is the contrary. It is not advisable at all to walk alone during the night time, especially in the old quarter. Taking some precautions during the visit is advisable, just common sense. Don't hang around in dark areas; try not to look like the typical tourist, etc.
The lower end of the street toward the Mardin Kapı, the Mardin Gate, is pretty dark and can be dangerous at night. Do not become prey to pickpockets who seem to hang around there.
The modern part of Diyarbakir is very much safer.
However, Diyarbakir seems to have recovered from the old times and the police is trying its best to provide a high level of security. So don't let you scare off from some issues mentioned above, as the city itself is still a jewel among others in eastern turkey, offering an amazing and unforgettable charm. Tourist crowds are still tending more to Mardin (1h away), so enjoy having the city mostly for your own.