Too add to what /u/esfandiyar2 said about Tehran Metro, it's a very simple layout. The one he has linked is a bit out dated, as more lines and stations are added.While I was in Iran, I used "Iran Metro" app. It's very helpful Because it overlays the Metro line with the city map provided by Google, so you know physically where the stations are located in the city and whats near it.
I ripped the apk and loaded it here, if you want to side load it into your Android phone.
http://www.filedropper.com/iranmetroirblogchamecoiranmetro15119-01
Unfornately, it's mostly Farsi, so I made a "guide" here to get the overlay. (First page is only for picking the city, and doing that only once).
This app is in both Farsi and English, but doesn't have that over lay.
http://www.filedropper.com/showdownload.php/tehranmetrocofardadandroidmetro12471
I also recommend downloading a local offline map via Google Maps app or HERE app, so you can use it offline if you don't have access to a data plan or WIFI.
Now, some places that I recommend seeing can be easily accessed through LINE 1 of Tehran's Metro. I would say:
1) Get off the Panzdah Khordad station, also spell 15th of Khordad, and visit Tehran's Grand Bazaar. This is a historic Bazaar, that was built at least 200 years ago and still retains it's old fabric and literally the bricks used to build the Bazaar. Today, the Bazaar is buzzing with buyers and sellers while it has kept it's old texture, offering modern items for sale, blending into an interesting atmosphere where the old meets the new. Also, there is a carriage ride that takes you from one end of the Bazaar to the other end (in the street, not the Bazaar itself). Great place to buy cheap souvenirs also.
2) The great thing about visiting the Bazaar, you can walk across the street (literally 3 minutes) to Golestan Palace. This historic palace is open to the public for viewing. You get to walk the great halls that once were only for royalty. While walking the halls, they have put up the gifts that were given from European royalties to the Iranian Shah. This also makes it into a museum, as many historical items and pictures are on display. I do believe they have a guided tour in English (99% sure).
UNESCO has given it world heritage status. Here is what UNESCO has written about it.
3) After that, ride the metro again towards Tajrish and take the 2nd station off, called Sa'adi station.