Belfast is a very historical town famous for many aspects of its history. One of the most famous things to come from Belfast would be the Titanic, which was built at the Belfast docks by the great shipbuilders Harland and Wolfe. You can still see "David and Goliath" there, the two largest cranes in the world.
You can also visit Belfast Zoo, Belfast Castle, Stormount, the main government building, the Botanic Gardens with beautiful greenery, the Waterfront Hall, the Odyssey (which is a huge complex with bars, restaurants, two cinemas, three clubs, a bowling alley, and a children’s learning discovery center), the Hard Rock Café, and an arena used for concerts and home to the Belfast Giants ice hockey team.
Just a few miles away, you will find the Ulster Folk and Transport Museum where you can learn all about the history of Ulster and how people coped in the famine and how they travelled to America where they built new lives. It is definitely a must to visit for anyone with Irish heritage -- you will be walked through your ancestors’ lives in Ireland, shown the different types of homes they would have lived in, hear folklore from way back when, taste Irish cuisine families they would have eaten, be shown the ships they would have travelled in and the conditions they would have suffered, and then be taken to a typical home in America that they would have built for themselves. It really is an amazing experience with knowledgeable guides and fantastic storytellers who know how to spin a yarn.
You should also visit quaint bars for a taste of true Irish hospitality or for those a bit livelier at heart, there are lots of clubs for any taste in music.
Belfast is the capital city of Northern Ireland, so the shopping there is fantastic from quaint gift shops to large malls to exclusive boutiques.
Quick Tips:
For day trips, I would advise people to travel to the Ulster Folk and Transport Museum, the Odyssey, and Belfast Zoo. Entrance fees only apply to Belfast Zoo and the Ulster Folk and Transport Museum. The Odyssey has something for everyone.
Best Way To Get Around:
There is a city bus service, which will take you to most places in the city centre. There are always both private and public taxis available for hire (however, when the clubs let out at the weekend, they can be like gold dust).