Shah Abd al-Azeem
In Tehran there is a ziarat (Shah Abd al- Azeem) and in the same complex there are 2 others - Hazrat Hamze (a.s.) and Hazrat Tahir (a.s.). Ask the driver to stay with you for the whole trip – he should also take you to the airport afterwards.
If you have luggage the shrine people can store it for you – you don’t even need to ask. As you enter the shrine they will tell you you can’t enter with your luggage and show you where you need to deposit it. This is at the other end of the smallish courtyard. When I went to collect my luggage this time, I asked the security person where I could get a taxi to the airport, he told me the shrine has its own taxi service! This was very reasonably priced and saved having to wait around on the street.
The receipt they gave me is here and you may find it useful in case you want to find the office - which is quite some distance from the shrine and the route is through the market ... (show it to someone).
If you decide to stay overnight in Tehran then you can get to the ziarats etc. on the subway/underground (very easy to navigate). This is not only much cheaper than the taxi, but also much faster as well. Tehran traffic is very bad.
The station for Shah Abd al-Azeem (Shahr-e-Ray, I think) is a couple of stops before that – but you will have to take a taxi from there – but the ziarat is well known and the drivers should have no problems finding it.
Imam Khomeini
The station (Haram-e-Motahar) for Ayatollah Khomeini’s shrine is the last one on the same line as Taleghani station (the shrine is walking distance from the station in fact it is the only building outside the station). The actual visit should not take more than half an hour. At the time of my last visit (2007), there was a shopping mall under construction around the Shrine complex.
This Shrine can be visited on the way from Tehran to the airport (vice versa) or combined with a ziarat to the Shah Abd al-Azeem shrine which is not too far away.
Royal Palaces
There are a number of such palaces around Tehran and can make for an enjoyable excursion.
Sa'dabad Palace
This was constructed to house the Pahlavi family. A tour of this palace should take no more than half a day. There are extensive grounds around the palace and the Alborz mountains can make for a nice backdrop to pictures as well. Photography is currently (2008) allowed within the buildings. Photos I have taken of the palace are here. This website is dedicated to the Palace and has a lot of extensive information:
http://www.saadabadpalace.org/index_en.htm
Golestan Palace
"The oldest of the historic monuments in Tehran, the Golestan Palace (Palace of Flowers) belongs to a group of royal buildings that were once enclosed within the mud-thatched walls of Tehran’s Historic Arg (citadel)". Source & more information:
http://www.golestanpalace.ir/En_Site/collections/E-history.htm
"Niavaran Cultural - Historical Complex is situated in the north eastern part of Tehran (Shemiranat). Its formation dates back to the Qajar Dynasty. This Complex which has been changed to a museum after the Islamic Revolution was administered jointly with Sa’adabad Complex till 1378 AH (1999), and became independent in 1379 AH (2000). Presently, it is comprised of five museums (Niavaran Private Palace Museum, Ahmad Shahi Pavilion, Sahebqaranieh Palace, Jahan Nama museum and the private library), and other cultural, historical and natural attractions including the Blue Hall, Private Cinema, Jahan Nama Gallery, and Niavaran Garden". Source:
http://www.niavaranpalace.ir/English/home-english.htm