I traveled around Romania independently in 2015. It's a fascinating country. Rick has done a video on Romania, which you can watch on this website.
Public transportation is slow, and English is not particularly widely spoken, though I think the younger generation is likely to do better than middle-aged folks. Romanian is a Romance language, but it has been surrounded by Slavic languages for a long time, so if is not as similar to French, Spanish, Italian or Potuguese as one might expect.
Traveling independently in Romania requires something of an adventurous spirit. For example, as of 2015 there was a strange requirement for some bus trips that the passenger make a seat reservation by phone before the trip, then buy the ticket from the driver right before departure. You couldn't make the reservation online, and you couldn't simply go to the bus station ahead of time to make the seat reservation or buy a ticket in advance. The procedure was very odd and quite cumbersome for foreign visitors. I figured there was little likelihood of finding an English speaker answering the phone for a Romanian bus company, so I got help from a couple of Romanians.
I wanted to see Maramures and Bucovina, two rural areas where it was clear public transportation alone wasn't going to be adequate. I joined a two-day, small-group tour of Maramures organized by the Retro Hostel in Cluj-Napoca. It was excellent. The driver/guide's first name was Florin; his regular job was as a history teacher. At one time he was listed on either Get Your Guide or Tours by Locals. The last time I checked, the Retro Hostel still had a long list of tour offerings on its website. You don't have to be staying at the hostel to take one of those tours, and I wouldn't be surprised if the hostel was wiling to connect you to one or more suitable guides so you could have a private tour. The hostel's tours run on demand, rather than on preannounced dates. Most tourists don't have schedules flexible enough to hang around Cluj-Napoca, waiting to see which tours will run. Costs in Romania are very low, so a private tour should be an affordable option.
The one-day small-group tour of Bucovina I booked through a random Romanian travel agency was not outstanding, but it got me to the area I wanted to see. It departed from Suceava.
I believe there are some interesting museums in Bucharest, but I found the city not particularly visually appealing. Ceausescu amused himself by knocking down as many historic buildings in the capital as possible and replacing them with ugly, shoddy new construction. You have to move around the city a lot to find the scattered remaining nice buildings. It's a different story in many of the other Romanian cities. I thought Sibiu, Sighisoara, Brasov, Timisoara and Cluj-Napoca were all lovely.
