If you are interested in visiting old part of Tehran then 30 Tir is the best place to go.
To go to 30 Tir you can take a taxi, bus or Metro. If you start your journey from Khomeini street then First you should go to the National Arch of Tehran. This place is so beautiful and many Iranian historical movies were made here. There are some lovely buildings here that are superb for taking photos including foreign ministry of Iran. Also national museum of Iran is in this street but back to the main subject ( Visiting religious sites) you should walk to 30 Tir street.
Haim Synagogue
Well for exploring the First religious site you should go to Haim synagogue (find Iraj alley on the map). The building is 100 years old and it has some nice story behind it.
For example its interesting to know that Polish Jews stayed here during the second world war and they could practice their religion freely. This synagogue is the most well-known one in Tehran and it has a nice decoration inside.
(The Synagogue was built in 1913 by Solayman Haïm, the Jewish Iranian lexicographer and translator, in the era of Ahmad Shah Qajar) (Wikipedia)
Adrian Fire temple
The second place that you can visit is Zoroastrian fire temple. This building dated back to 1916 . This fire-place was made with the financial help of Parsian in India and Iranian Zoroastrian.
Outside of the building was made in the form of old Mansion but inside there is a simple room with a fire burning in it. This is the only fire temple in Tehran that is open to public.
On the right side of it there is Firooz Bahram school which is for Zoroastrian students which has a nice architect but unfortunately it is not open to public.
Maryam (Merry) church
The most well-known church in Tehran is in the villa street(Saint Sarkis Cathedral ) but this one is also interesting. There are some painting inside the main hall but the interior decoration is simple.
Outside of it in the backyard there is a small museum of Armenian artist and also picture of different Churches in Iran. Just turn right from the main entrance and you can see the museum. You should buy a ticket to visit it.
Ebrahim (Abraham) mosque
Well there are lots of mosques in different cities of Iran but this one worth mentioning because it is located in the same street with a synagogue, a fire temple and a church.( There are of course better and older mosques in Tehran.)
30 Tir street is one of my favorite streets in Tehran. What I introduced above is just the religious side of it. There are important historical places and Cafes in this street.
Van cafe with Christmas decoration
Recently some stalls and Van cafe( In the beginning of street from Khomeini side) sells coffee and tea so its fun to buy a snack and a drink from them and start your journey to your destinations.
Unfortunately you can not take photos inside Adrian fire temple and Maryam church.