It is hard to select the most important cultural tips of Iasi. Many writers lived here and their houses still exist. In the picture you can see Ion Creanga small house that it is preserved here. This writer lived between 1839-1889 and almost 30 years in Iasi.
You may spend a traditional Romanian night at 'Bolta Rece' restaurant and you will be tempted to enter in 'Sonet Vila' too which is nearby.
I am not sure that this is a cultural tip, but on the theory that bookstores stock great literature, poetry, drama, etc., I will risk it: just to the west of the Hotel Traian is Junimea (named after a famous 19th century literary circle), reputed to be one of the best bookstores in the entire country! If you are from America, get the notion of a Border's or Barnes and Noble superstore out of your head. That's not a fair comparison (and you know it!). With the exception of Humanitas in Bucharest, I must agree. The store, though not large, has a wonderful selection (though, as also in Bucharest, even Romanian authors in English are rare).
You must visit Ion Creanga house (placed in Ticau area). You will meet the special atmosphere of OLD ROMANIA - hard to describe in words. This 'rustic air' is almost forgotten. Only in the Romanian villages you may find it exactly the same. . .