Peter Quill: You had known Peter was planning something when he had been avoiding you all day. You just didn't expect him to ask you out. It was a little weird for you - he was like your brother - but you went out with him so you didn't hurt his feelings. He took you out dancing and you had a great time. You danced the night away and soon you were the only people left on the dance floor, swaying to a slow song. It was the best date you'd ever been on.
Drax: Subtly is not in Drax's nature that's for sure. You had barely gotten to know each other before he was trying to "court" you. You kept on putting off his offers until you were sure you liked him. When you finally said yes, he took you to an aquarium where you saw some of the weirdest fish ever. One spacefish had a tank in the ceiling and swam above your heads. Drax lifted you onto his shoulders so you could press your hands to the glass. Overall you had a great time and he adored how excitable you were.
Rocket: He had been hinting at taking you out for months but when he asked you plainly if you wanted to go on a date with him, he promised to take you out the next planet they stopped, which happened to be Xandar. They were having a huge music festival and you carried Rocket on your shoulders through the crowds. You danced and sang along to the music while Rocket just stared at you. You were quiet and reserved on the Milano, but seeing you like this, he wanted to always see you happy and smiling.
Groot: Rocket wanted to come, but Groot made him stay behind and while there was a bit of a communication issue, you both enjoyed the walk you had together. It was a nature walk on a very popular tourist planet and it reminded you of your home world.
Yondu: Although you never knew it, Yondu had taken you out on several dates before you officially became his girlfriend. Whether it was getting a bite to eat or getting into fights, he considered them all dates and you never noticed until he shrugged off some flirt, calling you his date.