You can just go in and take pictures of the pretty fort but it's 3 AED to get into the museum. If you've already been to other museums (like Dubai Museum), you might think this one is a bit rundown by comparison. There are some archaeological stuff though, if you're interested. If you only have time for one museum, I would first go to Jahili Fort (just to walk through the fort and see the exhibit inside only if you have time) then talk a short walk through the park over to Palace Museum (see traditionally decorated rooms and such). Both are free and nice to stroll through. Then if you have time left, you can see this one. It is also a very short walk to the bus/taxi stop to Dubai/Abu Dhabi (takes 2 hours by bus to get there).
