Persepolis is a city near Shiraz, in Fars Province. Is an ancient capital city of the Persian Empire and one of the greatest cities in the Middle East at the height of the empire. It was sacked by Alexander The Great. Much of the foundations of the site however, remain. see wikipedia
You can reach Persepolis via car or taxi from central Shiraz or alternatively take a bus to Marvdasht and a savari to Naqsh-e-Rostam. At the bus station, the savaris demand around 10000 IRR, but a bit further off the price drops to 3000 IRR.
You can wonder around the ancient site and the famous 100 pillar hall. You are literally in touch distance of much of the ruins and statues, however try not to touch and potentially damage the ruins.
From any number of artifacts in the gift shop.
You can bring some food with you and have a picnic in the nearby grounds or eat at the nearby restaurant.
Alcohol is illegal in Iran. Bring lots of bottled water.
Near Persepolis are located ancient tombs housing royalty. You can also see an ancient Zorostrianst so named 'fire temple'.