I have been to Kyiv and Odesa. The plans were to spend orthodox Christmas this year in Lviv, but an emergency at the office cut my trip short and we had to return before we got to Lviv. Interestingly enough we went from Budapest to Kyiv, like you are planning. (our second home is in Budapest)
Did i like Kyiv? Absolutely. I will tell you why in a PM.
Logistically UIA is a very decent airline and you can fly them or you can fly WIzz. During my trip which included Kyiv and Odesa (really worth the time; especially if you are under 40), we used both of the airports and both were a bit disorganized but that isn't uncommon in that part of the world. Reminded me of the old Budapest airport.
In Kyiv we stayed at the Senator Hotel Maidan. It is a short block in one direction to Nezalezhnosti Square (the famous "Maidan") and Khreschatyk St (shopping, restaurants, great Stalinist architecture) and just a few minutes walk in the other direction to Sofiyivska Square and St. Sofia's Cathedral
We hired a guide and was pretty happy we did. Things are cheaper there so its pretty affordable. Let me know if you are interested.
Good chance we will attempt to get to Lviv again in May.