I like some traditional persian events or festivals like Persian new year, Yalda night or Chaharshanbe Soori.Iran has very family oriented culture which can be easily seen in their traditional events.
Persian foods are delicious and persian sweets are magic. I like frequent use of pomegranate, nuts,saffron and different herbs in persian cooking.I like persian rich(from north) it has great scent.
Persian literature is rich and mysterious in some ways.I love persian language and feel lucky to know it. The beauty of old poems are mind blowing for me.
Iran has vast variety of culture and traditions which can be so interesting for people who are interested like me.Sometimes even in unknown small villages you can see very interesting historical things. There is always something new to find out in every corner.
I like lots of historical monuments and the history behind them.
I personally like north of Iran so much....beautiful forest and nature.
Another thing which I like so much is persian carpets and rugs... sometimes the story behind how they generation after generation make these stuff make them even more precious. every symbol they use in rugs or carpets has their own story.
I like Iran's turquoise stuff too :-)
Its a long list and I can continue for a long time, But
What I dislike is basically everything happened/still happening to this country in the last 40 years.