Airline rules clearly indicated that the crew rest areas are only to be used by the crew, you usually find placards stating that on the doors to these areas. Anyway that doesn't mean it is not possible. These areas are not considered to be high risk areas or so, they contain bunks, emergency equipment and in some cases a seat or two. You can ask the cabin crew nicely and they will let you take a peek. I have done that many times. In the other hand, the crew rest areas for cockpit crew are off the limits and no one is allowed there even cabin crew, that's due to many reasons one of them is they are usually located next to the cockpit itself or in some cases the entrance to it can share the same door with the cockpit.
Now, you need to know what aircrafts have these rest areas:
777-200: they are called LCRC or lower crew rest compartment and contain 6 bunks usually. This is one of the ugliest crew rest areas, this compartment is a removable cargo compartment which can be installed or removed depending on the flight and crew legality. These compartments are tight and not usable on ground, you need to open a hatch on the floor to access it, the air flow will only start after take off, they are also usually hot. I personally hate them and I prefer a passenger seat over them. They are located next to R3 door (middle of the airplane, right side) and the access door is visible to passengers, it will be hard for the crew to let you go in. Also, it requires a key to open it.
777-300 : they are called OFAR or (overhead flight attendant rest area) and contain 8 bunks usually. They are so beautiful and big in size. Also bunks are big and makes you feel like home. The access door is located in front of L5 door (aft of the airplane, left side). The door needs a combination to be opened and only the crew know it. This will be easy for the crew to let you in, since no passengers will be able to see you when you are going up.
747-400: are one of the first planes to provide a designated cabin crew rest areas. They are located aft of R5 door (aft right side of the plane). They contain 6-8 bunks usually, sometimes two seats as well. It is large and well ventilated.
A380: it has two rest areas for the cabin crew. one in the middle and one at the back. It can also have three (depending on the airlines).
Remember, ask the cabin crew after the last service in the flight, because after the last service usually no more rest times for cabin crew and the bunks will be empty. Ask nicely and for sure they will let you see it.