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).