You can stay in hostels and enjoy the local food and traditions. Some of the most enjoyed places are Maramures, Tara Fagarasului, North of Moldovia.
For more information, check the following sites:
If you like to travel alone, you can take food and a tent to the mountains or the Danube Delta. Try to have a mobile phone with you and to remain in contact with someone from your hotel or chalet in case of a medical emergency or accident.