To do this museum justice, you should plan to spend 2-3 hours here. That means you will be on your feet for a long time: walking, standing, climbing stairs. Make sure to wear comfortable, supportive shoes.
Expect to check any bags you happen to be carrying. The bag check room is located on the ground floor, at the back of the lobby. This service is safe and free.
At the present time, photos and video are not allowed in any part of the museum. I have been at the museum when they were allowing photos on the top floor, but this is inconsistent. You need to ask one of the numerous “hosts” (available on each floor) about the photo policy at the time of your visit.
The facilities are state of the art, with plenty of restrooms and a grand café where weary visitors can rest their feet and relax with a coffee. The prices are high, but not exorbitant. The second-floor bookstore has an excellent selection of books on the Acropolis and its buildings. There is even a guide book to the museum itself that comes in two flavors: short or long.
Read my post on Areopagus: Accessibility. The bottom line is this site is steep, slippery, and unsafe. Though the views and the stories make a visit worthwhile, a broken ankle (or neck!) could put a serious crimp in your Greece trip.
Wear good shoes and watch your step. Not only are the original steps worn smooth, but the surface of the summit is uneven and pitted—a likely place to catch your toe and cause a tumble. As long as you are careful, the Areopagus should not pose a problem for most people. If you struggle with any kind of balance or walking problem, I would not attempt this site.
This site is ungated, which means a visit is free of charge and the site is accessible 24/7. However, try to time your visit for the morning or early evening—when the sun is not so intense and light for photographs is optimized. There are some great vistas here, including both ancient and more modern sights. If you have a tripod, this would be a good place to put it to use.
At the foot of the hill, there are benches in a lovely shaded spot … if you’d like to sit and contemplate for a while. If you bring your New Testament, this would make a great place to read about Paul’s visit to Athens (Acts 17:16-34—which mentions both the agora and the Areopagus). Paul’s speech to the Areopagus Council is commemorated with a bronze plaque at the base of the hill. Unfortunately, unless you can read Koine Greek, you will only be able to pick out scattered words like “Paulos” and “Athenaioi.”
Water and snacks are available at the nearby Acropolis ticket gate. There is also a bag-check room, restrooms, and a water fountain just a few yards away from the Areopagus.
The collection is arranged chronologically, with the oldest artifacts near the entrance and the newest near the exit.
Like the agora, the Agora Museum requires some kind of guide—person, book, or audio—to make sense of the artifacts on display. If you don’t know 
what you’re looking at, if you can’t listen to the stories and understand the history, you won’t get much from a visit here. There is the occasional wall text and informative caption available in the museum, but you can’t count on these to tell the whole story.
You should devote at least half an hour to this collection. With the right information, you can profitably spend an hour or two.
You will be asked to check larger rucksacks and bags before entering the museum. The check room is located at the southern end of the Stoa of Attalos.
Water fountain and restrooms are located in the Stoa of Attalos—on the north end. Although there are no benches in the museum itself, you can step out into the Stoa for a rest-break on one of the benches located along the central spine of columns.
Videos and photos are allowed inside the museum. But, please, no flash or artificial lighting.
More than most sites in Athens, the agora requires some kind of guide: person, book, or audio. If you don’t know what you’re looking at, if you can’t listen to the stories and understand the history, you won’t get much from a visit here.
With a guide, you should plan on spending at least an hour at the agora. I’ve spent half a day here and enjoyed every minute. The more you know (or, at least, the more your guide knows), the more enjoyable your time here will be.
You will be asked to check larger rucksacks and bags either at the ticket booth or (more likely) at the Stoa of Attalos.
Wear comfortable shoes with firm ankle support. Much of your walking will be “off trail” on this site, so watch your step carefully. It would be easy to turn an ankle or take a tumble here.
Water fountain and restrooms are located in the Stoa of Attalos—on the north end.
Videos and photos are allowed throughout the site. Because of the poor state of preservation of many of the buildings here, good lighting will be crucial to good pictures. Try to come in the morning or evening to get shadow lines and some contrast in your photos.
