I'm sharing a wonderfully informative email by Alan Casey, an Irishman I met in Korea. He is married to an Iranian.

As for things to do and places to see in Tehran, I would recommend the

 - Golestan Palace in the middle of Tehan. This was the palace of the ruling
Qajar dynasty which ruled Iran around the end of the 19th century
immediately before the Pahlavis came to power.

 - the Pahlavi (ie. the Shahs) palaces in the north of Tehran, namely
Nievarand and Sadabad. Interestingly for me anyway, the mullahs have
retained these monuments to decadence and opulence as tourist sites for the
public. You can see rooms where the Shah hosted foreign heads of state such
as Nixon, the Queen, et al. Enjoy a non-alcoholic beer in the grounds of

 - the main Bazaar in the middle of Tehran, close to Golestan Palace. Has to
be seen to be believed.

 - the mosque right beside the bazaar. Not as spectacular as the mosques of
Isfahan, but worth seeing nonetheless.

 - the house where Khomeini lived. Was interesting for me anyway -  a very
modest little house in the north of Tehran.

 - Bobby Sands street near the British Embassy, if you know your Irish

 - the compound where the US embassy used to be - not much to see here, but
maybe if you recall the hostage crisis, then you might want to see it.

 - outdoor restaurants in the north of Tehran in the foothills of the
mountains. Great place to sit and seat and watch the world go by.

 Places I haven't been to in Tehran but which might be worth seeing are:

 - the mausoleum of Khomeini to the south of Tehran on the way to the new
airport, called, surprise, surprise, Imaam Khomeini international airport!

 - jewelly museum, we meant to go and see it once, but we hadn't time.

 - Azadi tower built by the Shah. It's one of the more recognizable
landmarks in Tehran.

As for general info, remember that you can't wear shorts in Tehran. Sandals
are fine though. Booze while illegal, can be obtained relatively easily if
you in the company of Iranians. The Armenians normally supply the booze.
Basically it's like ringing for a take-away when you order booze. Try and
sample the local vodka, arak. You can get anything you want - the government
are probably secretly siphoning off their cut from the importation of booze
- it's all a bit of a sham really.