Translation:I will play with her today.
"Today I hang out with my girlfriend" Is accepted and in my opinion the most accurate interpretation. "Today I play with her" Is weird to me because if you are familiar with your playmate why use a pronoun? And also in english playing is most often used (in the meaning of 遊ぶ) when playing with preteens or younger. I'm no Japanese guru. English is my second language.