There are a lot of couples who find that they really enjoy sharing an afternoon picnic; there are a lot of ways to do such a picnic, as you can do it at a nearby lake or park, or can travel out to a more distant location for some true peace and quiet together - but regardless of what the two of you do for your picnic, the main thing is being together outdoors, with a picnic blanket, a basket of food, and an open invitation to relax together.
Another thing that a lot of couples find to be "fun" as well as being "outside the ordinary" is making time for something cultural, whether it is a museum, a play, an art show, a book reading, or something else; this can be a great way for you and your significant other to be alone inside a crowd of people, enjoying something fresh together.
And of course, another thing that is always great to do is for you to surprise your significant other - and one of the best surprises is an overnight stay at a lake, at the beach, or at a bed & breakfast; make sure your significant other does not have plans on the weekend night in question, then pack their bags for them when they are not around, and when they get home, let them know you are going out of town!
The main theme in all these ideas is doing something out of the ordinary, and doing it together; as long as you are searching for things that accomplish these two goals, you should be able to create plenty of fun with your significant other.