Shall we date? Sengoku Darling: Choose your Destination (2014)

The story takes place in the Sengoku Period, a warring era of never-ending social upheaval and military conflict. You, the heroine, is a princess of a small yet peaceful province. With your father in bad health and no son to take over the province, you are told to go on a journey to see through the world around you and find a strong province to ally with. For that, you head to the capital city of Kyoto together with your guard, Kojiro Sasaki, for information and chance to meet with strong warlords.
Life outside your own castle is not easy, but as you spend your life in the foreign land of your choice, you get to know more of the warlords living there. And eventually, the seed of love blooms into a transient flower...