Compared to Latin America security in the region is far better, you've got nothing to worry about on that front.
That said, the political situation will quite possibly prevent you from going exactly around the shore of the Black Sea.
Just a few tips from someone who has done a very similar trip....
- The only border crossing you can rely upon between Georgia and Russia is the one on the Georgian Military Highway, crossing at a post know as Kazbegi / Verkhniy Lars.
- It IS possible to drive into Abkhazia from Georgia and then into Russia (I have done it), but it is NOT possible to go Russia - Abkhazia - Gerogia at all. Any entry into Abkhazia is dependent on the whim of the Abkhazian Foreign Ministry who you should contact before reaching Abkhazia, and permission to enter is not guaranteed. If this sounds like a hassle, or if you have no idea what / where Abkhazia is, it's better to go via the proper Georgian border crossing I mentioned above.
- Donestk and Luhansk regions of Ukraine are no-go. That means the furthest east you can realistically cross the Russia - Ukraine border is just south of the Russian city of Belgorod, which leads to Kharkiv, and is safe.
- No problems with Ukraine - Moldova
- Romania is a country where you need to watch your stuff, and as I found out (had my tent slashed and 'important' bag stolen in the night camping in a national park), even way into the countryside you need to be on guard. Personally I would spend my time in Moldova and the Ukrainian Carpathians which are cheaper, friendlier and just as interesting as Romania IMO
- Bulgaria is not a country I know much about, but of all the EU countries it is probably my favourite.
- If you're a US (or UK or Canadaian) passport holder you can forget about going to Iran unless you book a personalised tour, which is obviously very expensive, takes a lot of organising, and totally ruins your freedom of movement.
I've written about Georgia and Abkhazia (and plenty more) here:
Stage 19 – Azerbaijan, Georgia & Abkhazia: The South Caucasus | EurasiaOverland
PM me if you need any further information
Good luck
EO