There are a good amount of methods of transportation that you can use to get around Kyiv:
For 8 UAH (about $.25 USD) you can purchase a one-way tram ticket. Trams come approximately every 15 minutes and are fairly speedy. You buy your ticket on a tram and then use a machine on the tram to punch holes in the ticket to show that you are using it for your trip.
Also 8 UAH (about $.25), you can purchase a one-way Metro ticket. Kyiv’s Metro is one of the deepest metros in the world and is super fast.
Another option is the city bus, which I have not yet taken. I have heard that they run quite frequently and are faster than the tram.
Uber is super cheap here in Ukraine and I rarely have to wait more than 8 minutes for a ride. On average they have been around 4 minutes wait time for me. To get around town costs about 75-125 UAH (about $3-$5 USD) on average.
POV (A.K.A., your car):
We have a sturdy vehicle for road trips and weekend use. The issues with driving around Kyiv are there is rarely any on street parking (just make your own spot sidewalk parking) and the occasional parking garage has super tight parking spaces if they exist. Additionally, the streets are not in the best condition and you will be apologizing to your car for all the potholes that you will drive over. My advice, have very good shocks on your vehicle and bring whatever extra parts you anticipate needing replacement.