A list of locations (and customs) of interest in Romania: 

1. The "Merry Cemetery" in the village of Sapanta, Maramures region, up North. This open-air museum features colorful tombstones with naive paintings describing, in an original, unsolemn and sometimes hilarious manner, the persons buried there. Sapanta is a UNESCO World Heritage Site. The almost one hundred gothic-style wooden churches of Maramures, in the same region, are also a UNESCO World Heritage Site.

2. The eight Northern Churches and Monasteries in the Suceava County: Patrauti, Sucevita, Moldovita, Probota, Arbore, Voronet, Humor, St. John-the-New of Suceava (each one of them a UNESCO World Heritage Site), known for their EXTERIOR frescoes of bright and vivid colors. The churches date from the 15th and 16th century, and their exterior frescoes were meant to illustrate biblical scenes for the illiterate faithful. Among these churches, the intensely blue Voronet Monastery (easy access from Suceava) is also known as the Sistine Chapel of the East; most notably on account of the Last Judgement fresco on the West facade. The "Voronet blue" paint on the exterior facades -- best viewed on a rainy day -- is derived from lapis-lazuli and has entered the art lexicon, next to "Titian red" and "Veronese green".  A ninth monastery of interest in the area (without exterior frescoes, however) is Putna, the burial site of Stephen the Great of Moldavia.

3. The Danube Delta biosphere natural reserve; the best preserved river delta in Europe and the only Natural UNESCO World Heritage Site in Romania. With more than 3,000 square kilometers of wetlands and water (marshes, channels, streamlets, and lakes) in Romania alone, the Danube Delta is a magnet for migratory birds from six major eco-regions of the world, including the Mongolian, Arctic and Siberian. There are over 320 bird species found in the delta during the summer. The Delta may not be there much longer, so visit now if you can.

4. The "Medieval Festival" in Sighisoara. Sighisoara is one of the few Saxon citadels in Eastern Europe which are still inhabited. The citadel was built in 1191 by Saxon settlers; approximately 150 historical buildings are still inhabited. Every year in the last week of July, Sighisoara returns to the Middle Ages: knights in armor compete in tournaments, witch trials take place, minstrels sing their songs. Sighisoara is a UNESCO World Heritage Site.

5. Horezu, a non-traditional tourist destination: a historical rural area featuring unique architecture and original ceramics (on the UNESCO Intangible Cultural Heritage List since 2012). The nearby Horezu Monastery, dating from 1690, is a UNESCO designated World Heritage Site. 

6. The Lipscani District in Bucharest, the charming and pedestrian historical center (17th Century) of Bucharest. The Lipscani district is Bucharest's best bet for finding cool cafes, bohemian bars, inexpensive food, and live music venues. The area is also "rich in antique stores where all manner of obscure treasures can be procured at bargain basement prices, including communist memorabilia, old photographs, icons and antiquated apparatus." 

7. Romanians are apparently the only nation in the world to still mix water (sparkling water) in their wine, on occasion; a tradition inherited from Ancient Greece, where the dilution of wine with water was a mark of civilized behavior.  The Romanian term is "Spritz". 

8. The second largest building in the world (after the Pentagon) - The Parliament Palace in Bucharest. A gigantic North Korean-style building in what used to be a charming Parisian-style neighborhood; legacy of the communist dictatorship. No comment.

9. The Dacian Fortresses of the Orastie Mountains, in Transylvania, an unusual fusion of military and religious architectural techniques and concepts dating from year 906; including a most remarkable system for water distribution based on ceramic pipes. These six fortresses were built in the 1st century BC and AD as a defense against Roman invasion. Another UNESCO World Heritage Site.

10. OK, fine: the Bran Castle; marketed abroad as the home of the titular character in Bram Stoker's Dracula. However, there is no evidence that Stoker knew anything about this castle, which has only tangential associations with Vlad III a.k.a. Vlad Draculea, a.k.a. Vlad the Impaler, voivode of Wallachia and loose inspiration for Dracula.  

11. The Transfagarasan (or DN7C), the second-highest paved road in Romania. 90 kilometers (56 miles) of twists and hairpin turns run across the tallest sections of the Southern Carpathians, between the highest peak in the country, Moldoveanu (2 544m or 8 346'), and the second highest, Negoiu (2 535m or 8 317'), connecting Transylvania and Wallachia. DN7C was built in the early 1970s as a military strategic route: a preemptive measure against a potential invasion of Romania by the USSR.

12. The Monasteries of Neamt County, dating from the 14th, 15th and 16th century. The Neamt monasteries (Agapia, Varatec, Bistrita, Neamt, Secu, Sihastria, Sihla) are beautifully located among orchards and vineyards in the Neamt hills; some feature collections of medieval art, and some have been painted (or have icons painted) by Nicolae Grigorescu, one of the founders of modern Romanian painting. Active monks and nuns work the land and the surrounding farms; more than 300 nuns are, reportedly, within the Agapia Monastery alone. The "retired" nuns of Agapia live in little houses forming an arrestingly flowery hamlet around the monastery; some offer rooms to let. The Ceahlau National Park  in the same region is a popular hiking destination; while the Vanatori-Neamt Auroch Reserve nearby Targu Neamt features a rare collection of live European bisons.

13. The Prahova Valley, about 100km North of Bucharest, easy access by train; a popular destination for hikers, mountaineers, and winter sports fans. The resorts in the valley include Sinaia, Predeal, Busteni, Azuga and others. The Peles Castle near Sinaia is a beautiful Neo-Renaissance castle (now a museum) built  in 1873 by King Carol I of Romania.