I toured in Romania in '21 and I enjoyed it very much, exceeded my expectations even. Great scenery, lots of history and culture and exotic enough (for a country belonging to the EU) to keep things exciting.
Top regions for me: hilly Maramures, on the northern border with Ukraine. Famous for it's wooden churches and the part of Romania where old traditions seem to resist disappearing most successfully.
The Danube delta. East of Tulcea there are virtually no more roads and boats replace cars, but you're still 70 km away from the shoreline proper. If you're a bird watcher, this region will blow your mind.
And of course, Transsylvania, with old German villages,
weerkerken (fortified churches) and scary looking castles. Don't get bit! This region felt less touristy than I expected and I had a great time.
Crossing the Carpathians via one of the famous passes (Transfagarasan or Transalpina) is certainly impressive but you will not be alone. Avoid riding there during the weekend. Moldavia in the NE was nice too, a sparsely populated, agricultural area that felt a little forgotten, lots of secondary roads that not yet had been paved.
Romania has an extensive network of tertiary roads with only local traffic and that's where you want to ride. These roads will not often be in great shape and some of them are unpaved (which adds to the riding experience IMO). Some of the bigger roads have intense truck traffic and are downright dangerous, Romania is a poor country (again, for the EU) and public infrastructure tends to be on the shabby side (narrow bridges, crumbling shoulders full of debris etc). I don't recall any crazy or hostile driver behaviour though (unlike Albania or southern Italy), just stay clear of the main roads.
I travel with a tent and only occasionally take a room (like in Bucharest or Sibiu) so can't comment on the availability of accommodation. My guess is this won't be a problem except maybe in high summer in some of the more well-known places. Plenty of camp-sites were small (and fun), sometimes of the in-my-garden variant, which leads me to think that there might be a lot of locals renting out spare rooms.
