As I mentioned a bit in the "Language and Culture" section, Dublin is a lively city with a lot happening all of the time. It is built around the river Liffey which divides the north side and the south side of Dublin. The south side is seen as more posh and has most of the historical buildings while the north side is seen as having a more of a working class culture and some of it's areas are very international. There is also a large suburban area. In the inner city there are many museums. The National Museums of Ireland which include the Archaeology museum, the Natural History museum, and the Decorative Arts and History museum are all free. I would also recommend The Little Museum of Dublin. You have to pay a small fare to get in, but the guided tour is very good. There is also a nice free photographic gallery in Temple Bar. There are quite a few parks. Phoenix park in the west is the largest and have wild deer and forests, but also training fields. It is a great place to go for a run. The Botanical Gardens in the north are very beautiful. There is also St Stephens Green where many people go to have picnic when the weather is nice. There are pubs everywhere and most of them have a steady crowd. Some pubs like The Cobblestones, have live traditional music sessions. There are also many cafes and restaurants especially in the area a bit south of Temple bar. Temple bar is the main tourist site and is charming, however, it is very touristic and most students are there very rarely. Smithfield in the northwest is a cool up and coming neighborhood with nice coffee places and an alternative cinema called the The Lighthouse Cinema. The area around Trinity is in general pretty and historical. The weather isn't the best, the winter is quite mild compared to Swedish winters. but unfortunately it doesn't really get hot in the summer. It is a much more moderate climate with quite a lot of rain.
Dublin has beautiful coastal suburbs. Howth is a popular tourist destination and has a lovely hike close to the ocean. Hiking between Greystone and Bray is also popular and I would recommend visiting the town of Dun Laoghaire just by the sea. You can reach all of these places with the local commuter train, the DART. It only takes 20min or 30min from the main central stations.
Trinity has many organisations and societies which are possible to join. The Hiking society, for example, takes you to different hiking destinations in Ireland (usually close to Dublin) for a small fee. Rugby and cricket are played regularly on the fields of the college and the university has many sport teams you can join. Trinity also hosts formal dinners throughout the year, but it can be very expensive and you have to keep a lookout for when the tickets are sold. There are also smaller social events which are happening through out the year. The largest social event of the year at Trinity occurs usually in April, The Trinity Ball. For that night the campus gets closed off and only the people with a ticket are allowed in. Multiple stages are set up all around the campus and everyone dresses up in formal dresses and suits. Throughout the night there are many different bands playing on the different stages. This year George Ezra was playing on the main stage. Unfortunately I didn't get a ticket. Everyone wants a ticket so they are hard to get and you will probably have to wait in line for hours to get them. So if you really want to go, prepare yourself in advance! Since I was working in the lab the entire term, I did not have the same exposure to the student life as someone who would do courses at Trinity. I became friends with the students in the lab and I was lucky with my housing and got most of my friends through there or through trips I had done around Ireland. The campus of Trinity is beautiful and students can go in to the Old Library for free and bring three guests. It's one of Dublin's most popular tourist attractions.
I traveled around Ireland during some of my weekends, mostly with people from my house. Bus Éireann is the main bus company in Ireland. They are not too expensive and cover a lot of Ireland. You can also take the train which is usually more expensive, but takes a shorter time. I traveled to the West Coast on a few different occasions. It's stunning, especially by The Wild Atlantic Way. I went to the picturesque town of Dingle by the water and also visited the tiny village of Annascaul. I took a guided bus tour around the Ring of Kerry and visited Killarney. Guided bus trips can be an easy quite cheap way of visiting different places, however, you have very little freedom so if it's possible to go on your own, I would recommend going on your own (preferably with some friends). Kilkenny is a quaint medieval town which you could visit as a day trip with a large castle. Galway is very charming and you have to visit the Cliffs of Moher. The Aran islands are very unique and can offer you a chance of hearing Irish spoken naturally by people who have it as a mother tongue. I never made it to Northern Ireland, but Belfast is only roughly 3 hours from Dublin and the Giant Causeways are a major tourist attraction.