Why dont you try looking at internal flights with Pegasus http://www.flypgs.com
. They are a very good company.
they have daily flights from Istanbul Sabiha Gokcen airport to Gaziantep. I just bought mine for about 30 TL, less than the bus fare! Gaziantep is about 2hours from Urfa. You could also fly with Pegasus to Diyarbarkir. I think that the Urfa airport is only used by turkish airlines, which have much higher fares than the low cost airlines.
As I've never been in Urfa I cant recommend a place to stay. I'm myself trying to find a hotel in Antep but it's not as easy in that part of turkey to even get a hotel to respond to you!