The northern part of Srilanka is not so much a tourist place considering the fact it has been destroyed by civil war for a long time. Before the war, the area was well developed. The largest city Jaffna is a newly built and I would strongly recommend to all to visit for the cultural, architectural differences. Jaffna Fort, Clock Tower, The Oldest Library are must! In case to refresh yourself, a couple of beautiful beaches surrounding the north area or to reach the most northern point. Many temples characterize Hinduism for Tamil Hindu Srilankans who are the majority. You can also travel to the nearest small islands and make a nice trip by boats/ferry. There are many trains from Colombo to reach North, even Express trains which are comfortable and luxurious. During the ride, you can see some effected areas by the civil war.
I am still adding new pictures and experiences, so stay in touch!

First train
The first train which left Jaffna after the Civil War. The symbol of connecting previously divided areas.

Public library
This library was one of the biggest in Asia until it burned in the 20th century as a violent act. A few years ago was newly rebuilt. At the front is a statue of Saraswati, the Hindu goddess of learning.
Location.

Hindu temples
Many Hindu temples are to see as Nallur Kandiswamy Hindu temple, one of the oldest as well. This place of worship, painted in gold, is breathing with history. Men have to be topless, and women cover their knees and arms.
Location.

Small islands
As part of your journey around the North, you can visit any of the closest small islands. You can reach some island via roads and bridges, to other you have to take a boat or a ferry.

Near beaches
For example, Keerimalai and Kankesanthurai beaches in the North are worth to visit. I paid some small fee. The beaches are sandy and mostly visited by locals.

Location.

Local markets
Local markets are also very typical. You can buy everything here from vegetables, fruits, bread, food, dry fish, accessories, gifts, kitchen equipment etc.

Prices for trains
You can see the list of prices for trains from Jaffna central train station.

Train schedule
Train schedule for Jaffna-Colombo Fort, Colombo Fort-Jaffna.
Let me know whether you need help.
