I found out that they have closed the line west of Pripyat...and the line from Slavutich to Pripyat is only for plant workers.
Unca ~ It makes sense that they've restricted that line and reserved it for the SIP personnel commuting from Slavutich to the plant. I really hope you're successful in getting close up, and I'd like to hear about it once you do.
I don't have any pointers for you in Bulgaria or Romania...never been outside their airports. In Moldova, you're fine as long you avoid the Transdniestr region, as it's not yankee-friendly. If you're coming into Ukraine through Moldova, you'll be passing up much of what is good about Ukraine...the Black Sea coast. I guess you can always head north (toward Chernobyl) and back down to the coast.
Not sure if you're on a cultural trip, party trip, or a little of both, but I'll go over a couple places. To keep this post from being a novel, I'll leave you to your Google devices to see if any of these are worthwhile...
I didn't have much free time in Kiev, but I can recommend the Pechersk Lavra. Never seen anything like it before. It is a tourist stop, but without the tour guides, so you won't need Benadryl for your allergy. You'll need to look up some history of the monks, saints and mummies before you go, or it won't really mean much to you. Once there, you'll be hard-pressed for information unless your on top of your Russian-ese.
Sofiyivsky Park in Uman (half-way between Kiev and Odessa) is quite something, but maybe not for two grown men to visit. Direct rail line from Kiev-Uman-Odessa. Given your travels, you can probably forgo the air-conditioned railcar!
Odessa is by far my favorite, but I'm biased after living there nearly five years. It's a place to just relax. The city center is easy for us (English menus and such) and the beaches are what attract most. Arcadia is the resort area of Odessa and at least worth a visit. If you or your nephew happen to also be allergic to topless Ukrainian women, you may want to avoid the beaches.

Anywhere on Crimea is great. You can get to Crimea via bus, train, or boat from Odessa. Sevastopol has great naval history and Yalta is a large attraction, but will be very crowded (translates to paying too much for a place to stay). I prefer Feodosiya as it's not as crowded. You can cross over into Russia via ferry from Kerch (visa needed for Russia).
Geez...I hope you haven't already started this trip or else this will become a big list of things you COULD have done.
Safe travels!