The northeastern region of Romania, near Ukraine and Moldova, is Bucovina. It's where you'll find the glorious painted monasteries. I took a one-day tour of that area starting from Suceava (not sure there's much to see in that city), and the guide was not outstanding. Or perhaps this area is just a bit more one-note than Maramures. The monasteries are really beautiful, but if I had time for only one of Maramures and Bucovina, I'd go to Maramures for sure.
I took a day-trip to Iasi but was underwhelmed. Pleasant enough university city, but I missed the beautiful medieval architecture in Timisoara, Cluj-Napoca, Sibiu and Brasov. Iasi has a botanical garden, but I didn't manage to get there.
I've read good things about the Danube delta. Definitely do some research, especially if you're interested in wildlife. I don't know anything about the beach situation. I think the Bulgarian coastline was preferred in the old days, but that may have been because Ceausescu was such a nut job.
Another place I didn't see is the Bulgarian border city of Ruse (on the rail line between Bucharest and Plovdiv). It's supposed to be a worthwhile stop.
The Romanian countryside is really pretty--lots of green, lots of hills. I suspect there aren't a lot of multi-lane highways, but I don't remember noticing that roads were in bad condition. Having a car would eliminate the tyranny of bus/train schedules from consideration, a major plus, but you have enough time that you'll be OK without a car. A plus of public transportation is that it will bring you in contact with English-speaking young locals. As I mentioned in my first post, I highly recommend a tour in the Maramures area. I think you'll miss a lot on your own by not knowing where to go to see the best carved-wood gateposts and the like.
Food in moderately-priced Romanian restaurants was unspectacular but OK. It may have been Rick who said that the locals can't afford to eat out, and that appeared to be the case. If you want interesting food, you may need to look to tourist-oriented restaurants. I'd caution you to engage your brain (as I did not) when considering take-away treats. I had a slice of tiramisu from a pastry shop in Cluj-Napoca that tasted like it came out of a chemical factory. I doubt that it had any dairy products in it. I should have realized that 1 euro was too little to pay. The widely-available bread rings (sort of like bagels 6" in diameter), on the other hand, were universally good. They come with different fillings and coatings, some savory and some sweet. I think they're called "covrigi", but you can just point. They're such a thing that many bakeries have windows open to the sidewalk to sell them hot out of the oven in the morning.
Handcrafts are relatively inexpensive in both Romania and Bulgaria. It was my impression that Romania sticks more to traditional designs (painted eggs, ceramics, embroidery). I did see embroidery that (to my totally uneducated eye) appeared to be local rather than imported from China.
You may be surprised that you can figure out a lot of signs in Romania. Romanian is a romance language. Unfortunately for people who've studied French/Spanish/etc., it has picked up a lot of Slavic influences (including word endings) from the surrounding languages, so being able to speak it will be a different matter.
Check weather stats. Fall will probably move in before you arrive. For me, that would be a good reason to have a rental car some of the time, but if it's very rainy, those 2-lane roads could be rather hazardous.
Rick's 2016 videos include one on Romania.