Check out a museum To "check out a museum" means to visit a museum together.
Celebrate an anniversary An "anniversary" is the day and month that is the exact day and month of a special event, such as the day two people got married. So to "celebrate an anniversary" means to do something special because it is an anniversary, such as to eat a meal at a special restaurant.
To have a fling To "have a fling" means to have a short, intense relationship with someone.
To ask someone out To "ask someone out" means to ask them if they want to go out on a date with you.
Go out To "go out" means to go out on a date with someone that you are romantically interested in.
Date To "date" means to go somewhere with someone you are attracted to in order to spend time together.