The nearest city from Craiova with airport is Bucharest (Bucuresti) which is also the capital. From the airport of Bucharest you can travel:
-by train with the price of 10Euro with the Intercity the duration being 2h 28'
-with the Rapid train-2h 50', same price
-or by bus with the same aproximate price, duration:4h 25', the distance between Bucharest and Craiova being 248 kilometres.

There is another city with airport situated in the west of Romania-Timisoara which is at a distance of 353 kilometres from Craiova. From there you can travel:
-by train-Intercity with 14Euro, duration 4h 53'
-by train-Rapid with 8,92 Euro, duration 5h 30'
-by bus (Atlassib or Trans Baco) with 10Euro, duration: 7h

For more information:

Mersul Trenurilor
Romania Travel
Atlassib

An extra meal costs around 8 or 10 euro's in a restaurant, cheaper if you are used to fast food.