There are no "cool backpacker hostels" near the airport. End of story. There are cool backpacker hostels in town. Mamallena is one such.
There is a bland, boring, character-free hotel which claims to be a hostel within sight of the airport exit rotary. Unless something has changed drastically recently, it's a perfectly acceptable place to stay if you need to catch an early flight. I've done this a couple of times. As an indication of how little it represents the cool backpacker ethos, the closest meal options are in the airport itself.
Hope that's helpful.
Mark