traveling from Slovakia into Ukraine then back....

If your plan is to rent a car in Austria (or Slovakia), you may have some trouble finding a company that will allow you to take their car all that way east.

My understanding is you can now go on an escorted tour into parts of Chernobyl (the abandoned town, not the actual ruined reactor complex). The area is surrounded by a huge "exclusion zone" which is fenced off with access controlled - you need a permit to enter. I don't think you can go on your own (and for good reason). IMHO it would be foolish to try to sneak in.

Personally, although I can see the appeal (and would be tempted) I don't think I'd go - too many unknowns and to many opportunities to dose yourself. Not a risk I would take - there are plenty of other places to take pictures.

Are you an AAA member? If so, can they advise on the driving part?
Chernobyl, well, I would at least look at what type of protective gear they use....then decide what your personal risk quotient is.....

My recent experience in Ukraine is very limited (as in 3 days), but I think hoping to make it to Kiev on the ground with stops for photography is way too optimistic. Today I traveled from Uzhgorod, Ukraine, which is practically in Slovakia, to Ivano-Frankivsk, also in Ukraine. The trip was 180 miles. The bus was scheduled to take 10 hours, but it managed to be 30 minutes late. How is that even possible, you may ask. The answer is, basically, potholes.

I'm sure the major roads between the very largest Ukrainian cities are in better shape, but for photography I assume you'll want to see the Carpathians, the wooden churches, etc.

You should also expect to lose time due to linguistic difficulties outside the tourist zones.

I'm having a few issues with this trip.
I just (a few hours ago) learned that I need to have a green card insurance paper for my car AND my current auto insurance does not provide that. SOOOO I'm looking into purchasing the insurance at the border (I've never done that, I don't know how to do that....)
ALSO to make it even a bit more challenging - The car is registered / owned by my wife HOWEVER she is NOT going to be with me on this trip.

So --- does anyone have experience, or places I can research on how to do all this. I'm still game to try, and if I get turned around so-be-it but I don't want to be stuck somewhere.

The potholes, yeah - I've heard it's pretty rough on the roads out there.

Details I neglected to mention earlier.
The car -- it is MINE (my wifes)
It is insured/registered in Switzerland
Car is 2013 Subaru (nothing fancy here)

Day 4 in Ukraine, and the linguistic challenges continue as I travel through less-touristed cities. This trip would be quite difficult if I hadn't studied Russian for 4 years (albeit 45 years ago). Combine limited English facility with not much experience dealing with foreigners (so little practice at charades) and you get people who just rattle off several sentences of Ukrainian rather than a few key words. You have to keep asking different people until someone comes up with two words you can understand: the Ukrainian version of "other station". Who knew Ivano-Frankivsk has two bus stations? I don't usually have to be rescued by random English-speaking passers-by, but it's becoming a regular thing here. It all takes time.

Hot tip of the day: In addition to good road maps, be sure you're covered for city maps of the historic areas you might visit on foot. Print them off Google if you need to. I've stayed in three Ukrainian hotels. Only the first had a city map. I haven't seen a tourist office yet. There may be one here in Chernovtsi, but the hotel receptionist pleads ignorance.