How you can get here

By train – you can get acquainted with the schedule and buy tickets online here: http://e-kvytok.kiev.ua

Direct flights to Kharkiv:
from Istanbul - Pegasus http://www.flypgs.com/
from Antalya - Utair http://www.utair.ua/
from Warsaw and Kutaisi - Wizz air http://wizzair.com/
from Moscow – Aeroflot http://www.aeroflot.com/ и Utair http://www.utair.ua/
from Wien - Austrian airlines http://www.austrian.com/
from Barcelona - - Vueling Airlines http://www.vueling.com/

There are air lines that fly to and from Kiev from all around the world. A popular source for searching: https://www.anywayanyday.com/
You can get to Kharkiv to Kiev by plane of Ukraine International Airlines (http://www.flyuia.com/ and Utair http://www.utair.ua/) or direct trains Kiev-Kharkiv:

N 156 departes from Kiev at 06:20 – arrives to Kharkiv at 10:56
N 164 departes from Kiev at 18:08 – arrives to Kharkiv at 23:43
N 64 departes from Kiev at 22:23 – arrives to Kharkiv at 06:46

You can check the rules of crossing borders and custom regulations of Ukraine here: http://ukraine.visahq.com/customs/

There’re no mass riots in Kharkiv.