I was worried that a lot of things would be closed on a Friday in Ramadan and so planned an itinerary that could be done largely outdoors. It turned out that my worries were largely unfounded. While many places were shut, it was no worse than Sunday in a typical European city. Tourist attractions seemed to be open as normal and there were still plenty of booths selling drinks and snacks to fast-breakers like me.
My first stop was the Azardi tower. The Azardi tower is one of the most famous symbols of Iran. It was built in 1971 to celebrate the 2500th anniversary of the Persian Empire. There is a museum underneath with information about the different industries in Iran (aircraft, cars, robotics, mining, etc). At the top there is an observation deck that gives excellent views of the whole of Tehran and the mountains around it.
Having seen the mountains from afar, my next mission was to see them up close. Tehran runs right into the foothills of the Alborz mountains. In the future you should be able to get all the way to the hiking trails by metro, but for the moment, one needs to take a taxi for the final couple of miles.
One of the most notable things about the Mountains was that everyone was eating and drinking openly, even though it was a Friday in Ramadan. I wasn't able to get a good explanation from anyone about why this was beyond "it is hot".
As a tourist in Iran one is rarely alone since people are usually very keen to talk to you, befriend you and help you out. While hiking I was joined by a group of young Tehranis who were keen to talk to me. We talked about normal things that young men talk about. Girls (including the relative attractiveness of those around us), beer (and the frustrating difficulty of obtaining it in Iran), English Premiership football (allegiances were divided between Manchester United and Arsenal), pop music (English bands are apparently very popular), the TV series 24, and how many people actually fast at Ramadan (they thought most people didn't).
We also got to discussing Islam. They considered themselves to be Muslim, but weren't much into the praying and mosque-attending parts. When I asked what Islam meant to them, one person said "being good to people, and not smoking" (between puffs on a cigarette). The Islam that many people in Tehran practice seems about as fundamentalist as the Church of England.
Eventually two people from the group invited me to come back to their apartment to have dinner with them. I accepted and then fed me a delicious omelette-like thing made from eggs and tuna.