Afterwards, if you have time, I would stop in Cluj (Cluj-Napoca) too. It's a beautiful place, although very different to the ones I presented until now. Although having a history of more than 2000 years, its center is mostly populated by buildings from the 17th-19th century. A city with a large university, very very good for partying and all kinds of fun. Used to be the capital of of Principality/Voivodship/Kingdom of Transylvania for a long time.
I promised I would get back to Iasi (Jassy, one of the few Romanian cities apart from Bucharest that does have an English name), so here I am. It's another university town, that used to be the capital of the Principality of Moldova, a country that is now split between three modern states - around 50% in Romania (including Iasi, the "capital"), around 30% makes up the current Republic of Moldova, and around 20% is now in Ukraine (northern Bucovina aka N.Bukovine and Bugeac aka Budjak).
For a one-week trip to Romania, coming from the east, I would suggest the following itinerary:
Iasi - Bucharest - Sinaia - Brasov - Sibiu/Sighisoara - Cluj.
(OH CRAP, I just realized you said you're going SOUTH from Romania, and not West. In that case, reverse the itinerary, make it Iasi - Cluj - Sibiu/Sighisoara - Brasov - Sinaia - Bucharest)
You can spend 1-2 days in Bucharest and Iasi each, and one day in the others. It's worth the time, IMHO.
The itinerary marked with red goes through Sibiu rather than Sighisoara, but I'm REALLY NOT sure if this is the better choice. I honestly don't know which one to recommend.
The alternative itinerary in green goes through Sighisoara, and the other green spots are other interesting things that you can see:
- Timisoara, aka "the little Vienna", with beautiful Habsburg architecture and many things to do
- Craiova, with a newly-renovated old center
- Alba Iulia, small town but again, beautiful old center
- Hunedoara, with the largest Gothic-style castle in Romania:
Also, on the way to Brasov, you can make a little detour (less than 10 km, if my memory serves me right), to the Rasnov fortress, which is quite amazing and unique.
Anyway. Those would be my suggestions about various things to see in Romania, other than Bucharest.
Sounds interesting. Would you say it is worth forgoing something else for, or is it merely good in the same way everything else in Europe is?
That is a decision that only you can take. For me it was one of the best times in my life, but it doesn't mean it's that way for everybody.
Yeah, I was thinking that if I went to Bulgaria (on the way from Bucharest to Istanbul), I would go to Veliko Tarnovo, simply because it's right on the train line. But do trains actually stop near there on the way from Bucharest to Istanbul, or is much simpler to go direct from Romania to Turkey without that stop in the middle?
That is, again, only up to you to decide... I'd spend a day there, but that's just me.
So what exactly is there to see in Bucharest?
This deserves a whole new post. I'll come back to it sometime later.
@Squonk- Gah! So many pretty places to go! Would you think it possible to stay in Florence for, say, 3 nights, and see Florence, Pisa and Siena in that time?
@onedreamer- Turin sounds cool, looks pretty. I guess you could easily spend a couple of days there?
Wait wait wait, you're thinking of seeing Florence, Pisa and Siena in 3 days, and spending another couple of days only for Turin? No offense to onedreamer, but that's inconceivable, IMHO! Florence alone deserves a lot more than Turin, IMO! And Siena too! Do think this through - I mean, Turin is absolutely awesome, but Florence, Siena and Pisa...
I don't know, as I said, it's your choice - you will feel much more satisfied taking your own decisions.
I got that amber turned into a beautiful necklace which turned out to be a great mothers day present. 
I guess I'll see how it pans out.
