I am planning to spend 3 weeks in Turkey and Kurdistan.
I'm told the region is relatively small and I could feasibly stay in Van and explore from there. Is that wise? If not what other cites would be interesting and safe to use as bases?
I suppose that when talking about "Kurdistan" you have in mind the turkish part of Kurdistan. Note that "Kurdistan" is not a country nor is it a region of one single country.
I cannot agree with what you have been told. The region you have in mind is larger than you think. If you are driving on your own, which is perfectly feasible, your average speed will be about 60 kilometers per hour on the major axes. If you are traveling by bus, note that in this part of the country, the buses are less frequent than in western Turkey.
As an example, from Van to Doğubeyazıt (near Mount Ararat) is about 300 kilometers, a 5 hour drive in one direction ...
There is no reason to get stuck in Van or another place. Especially if you have three weeks at your disposal to discover the region (lucky you ... ;-) ). Okay, in eastern Turkey and south-eastern Turkey, the tourist infrastructure is not comparable to what can be found in the West or on the Mediterranean, but it is possible to find decent hotels.
This being said, if you are intersted in travelling to Turkey, a look at Turkey Travel Planner is highly recommended.
There was an earthquake in Van last month and there has been many smaller ones since then. Many buildings have collapsed and there are problems in the electricity network. So I definitely don't advise you to visit Van any time soon. However, it is a nice city with history and nature.
I do not know where exactly you mean by Kurdistan, but I suggest Adıyaman and Mardin if you'd like to visit the eastern part of Turkey. Mount Nemrut is the main touristic attraction of Adıyaman with huge statutes made in 62 BC, also watching sun rise there is lovely. Again, this season is not the best time to visit there due to cold weather. Mardin has such a unique architecture. You can find many mosques and churches, also high quality hand made and relatively cheap silver jewellery.