I think that one of the problems with modern museums is that they try to evoke some kind of mysterious atmosphere: in poorly-lit rooms, you can see only a couple of objects lying there, beautifully spotlighted, just looking mysterious. The illumination allows you to look at it from one point of view, but not from other angles. Photography is almost impossible. In other words, you cannot study the objects.
I get the impression that museums are now leaving this cul-de-sac, and return to decent displays. The Archaeological Museum of Tehran has never succumbed to ill-directed aestheticism, and this makes it, easily, one of the better museums dedicated to ancient culture.
This does not mean that there are no beautiful objects. The first part, dedicated to the Neolithicum and Bronze Ages, culminates in the pottery from Susa, which is just splendid. Recently, this part has been redesigned; several objects from the important excavations at Jiroft have been inserted, to name but one change.
Passing along a nice sculpture of a bovine from Choga Zanbil, you will reach the Iron Age, where you will find an Assyrian and an Urartaean inscription, and countless small objects. They are interesting, but your attention is drawn by the great relief next to it, from the northern stairs of the Apadana in Persepolis. Next to it, about half-way through the exhibition, is the statue of Darius from Susa (more…). I visited the museum yesterday with an Egyptologist, who was fascinated by the hieroglyphs.
There are some other Achaemenid remains, including several inscriptions (like this one) and some fine art. Here, you will also see a Penelope in wet-drapery style, taken to Persepolis by either Xerxes or Mardonius.
Compared to the Achaemenid age, the Greek, Parthian, and Sasanian ages are a bit underrepresented. From the Greek age is a fine bust of a Muse, from the Parthian age is a splendid bronze statue of a prince (one of the few remaining bronze statues from Antiquity), and from the Sasanian age are the spooky salt men and some mosaics from Bishapur, made by Antiochene artists.
The museum has a treasury that contains precious objects, made of silver and gold, but it is often closed. Asking for permission to get there is futile. In this aspect, the Tehran Museum suffers from the same error as western museums: it creates obstacles for students. I think this is inexcusable. There is simply no reason why a museum should hide its entire collection from people who have made an effort to get there.
This being said, the Tehran museum is really something special. Next to it is the museum of Islamic Art, which has not been open for quite some time; I remember that I liked it very much. Around the corner you will find the Ministry of Foreign Affairs, situated in a building that is inspired by the Persepolis Apadana; and around another corner, you will find a charming museum dedicated to fine art made of glass. If you have only one day in Tehran, spend it in this part of the city.
This museum was visited in 2004, 2005, 2008, 2009, 2010, 2011, 2012, 2013, 2014.