Short answer, you can hang a tapestry wherever you want. They are a great addition to bedrooms, living rooms, even bathrooms. What you should take into consideration, however, are the aesthetic and color scheme of the room, and the size of the walls.
Tapestries and wall hangings cover a large surface, so they can make or break the aesthetics of a room. If you don't know which room your tapestry will look best in, try out different placements until you find the one you like.
If you want your tapestry to fit in with your room seamlessly, try placing it directly above a couch or a bed, so the edge lower of the tapestry falls slightly behind it. This will make your room feel more cohesive.
If you want your tapestry to stand out, you should place it on a wall with plenty of space. Making tapestry the main wall decor with plenty of blank space around it will surely give it the attention it deserves.