Qom is one of the most holiest cities in Iran and the middle East and is entrenched in centuries of history. It is considered to be the "Jewel of Iran". The famous thing about Qom is the Fatima È Massummeh Shrine which is a highly respected shrine and a very clean place. Non-Muslims are allowed entry to the city.But, they are not allowed entry in the holy shrine unless with a Muslim companion or guide.
The nearest and most easily accessible international airport is Tehran's Imam Khomeini International Airport (IATA: IKA, ICAO: OIIE), which is due to replace the older Mehrabad International Airport (IATA: THR, ICAO: OIII).
Driving from Tehran might be a reasonable option, however, if you're worried about driving in Iran you can reserve a private bus to take you to Qom. After all, it is much safer to travel by private buses.
There is a pretty impressive bus and taxi system, which has many bus routes to Tehran and other cities. It is very cheap to travel by local buses in Qom. Private tour buses are generally much more expensive.
Qom has many carpet and sweet (candy) shops. Qom is famous for it's "sohan," a flat sweet biscuit made of pistachios and saffron. "Gaz", a nougat candy is also available. Qom is also known for the unique and beautiful silk rugs which are famous worldwide for their unique silk and patterns. Naturally, as one of Islam's holy cities there are numerous religious shops which sell religious books, versions of the Koran and compact discs.
There are lots of places to eat in Qom which range from old style Persian restaurants to international restaurants. Persian restaurants offer a more authentic cultural atmosphere than international restaurants.
In Qom, there are various cafes and fruit juice shops. Pomegranate juice is popular and is said to heal the sick. In the winter when it snows, hot chocolate and Persian tea (Chai) are available.
Qom is one of the holiest cities in Iran and the Middle East, and as such be aware that Islamic customs and values are more likely to be important here than elsewhere in Iran. Don't let this worry you at all, just ensure that you are respectful of religious and cultural practices and that you are dressed appropriately and modestly.
If you feel like visiting another quintessential Persian city, a few hundred kilometers away, you can visit Yazd which is an beautiful ancient city. Isfahan is another option and is a very beautiful city and is considered to be one of the oldest and most historic cities in the world.