Look for tickets to the theatre, circus and other events is beter before the trip to Ukraine. There are some tips how to choose the right ticket-selling websites.
Parter.UA, Concert.UA, Gastroli.UA – there are some really useful event search engines where you can pay for your tickets with your credit card. The only one big minus is the required ukrainian phone number. I suggest You take the number from the image on the top or contact to Your friends from Ukraine.
internet-bilet.ua – You can register on this website with Your local – british, american etc. – phone number, but You can’t buy selected tickets. On this website You can pay Your order if Your card is Visa or Mastercard of the Ukrainian Banks only. I cann’t help for that…
These are still not tested: