North towards Esfahan, Persepolis
From the city centre, take bus number 70 north-east on the Zand (main street). when it stops, at a bus terminal, take bus number 74, ans ask for the Qur'an Gate (Darveza Qu'ran). From there, walk up the road a little way and there is a big parking lot you can hitch from. if you catch a short ride from there, there is police checkpoint that you can also hitch from. for Persepolis, find a ride to Marv Dasht, which is easy enough. Persepolis is another 10km from there, and you may have to take a taxi (3000 tomans). Remember to walk under the Qu'ran Gate as you leave, it will apparently bless your journey (whether you believe in that stuff or not, it can't hurt).
To the road 86 From Imam Homeini sq (city center) take bus to Amir Kabir blvd. Then take bus number 94 or 48 and when they begin return, you need get out. You are on the road, just find a good position and hitch.