It's not just Republic of Ireland here, there is one more Ireland on this island: Northern Ireland which is a part of United Kingdom of Great Britain and Northern Ireland. A long time ago it was a single country, though something went wrong in history. In the Medieval time English people started emancipation of Ireland. They started to take over the land, set new rules and even replace the language with English. As a response Irish people made riots and rebellions.
All that resulted into separation of Ireland from United Kingdom. So in 1921 Republic of Ireland became a separate state. But part of Ireland where protestants were a majority didn't want a separation, they wanted to stay with UK, as on island protestants were a minority and they had some issues because of that before a separation and they saw a huge risk of getting it worse after it. So they decided to stay with UK. That's how Northern Ireland was created and Belfast city became it's capital.
By the way, Belfast received status of city only in 1888. It was granted by Queen Victoria. Though the status doesn't really bring some additional privileges. And there is no special criteria to receive it. ,Though in England it was traditionally given to towns with diocesan cathedrals. In Northern Ireland there are only 5 cities, and only 69 cities in the entire United Kingdom.
Belfast castle was build in 12 century inside the city. Though in 1708 in was burnt down. So Chichester family who owned the castle decided to build a new own in suburb. The building process was extremely slow (from 1811 to 1870) due to financial issues in the family. Later in 1934 castle was presented to the City of Belfast. So now it's open for public and visits are completely free.
Interior though is quite simple.
When you come to the city, there are some areas where it is strictly prohibited to drink alcohol. Otherwise one will be fined for 500 pounds. It's really a lot. Though this is a way they are fighting against drunk people in public.
Another thing which is really can be easily noted: everything is closed quite early. 5-6PM and it's closed. Still one can find a restaurant, but most of the shops is already unavailable.
Among different sightseeing places Albert Memorial Clock is quite interesting. Somehow it reminded me Big Ben :)
Underground street passes don't looks really friendly. Sometimes there are even some homeless people near the entrance. Somehow there is a feeling to avoid it at all.
Though in general city is clean.
Near city hall there is a huge display where they translate news. With sound. So if you have no TV at home you can come here and watch the news.
And of course Belfast is the city where RMS Titanic was built. Yes, that Titanic which sunk later. Irish people make really good money on it. They have a huge museum here, even the place where it was put on water is marked. And they make a guides here.
The weather in the end was not really good. Some drizzle. Though it was not that bad.
PS. The only thing I can't understand is why in United Kingdom they still use old fashioned separate hot and cold tap in public places? People already invented combined tap. It's really inconvenient to make a bath in public toilet (and not really hygienic imho). So I had to wash my hands either with cold only, either with hot only (if it was just a bit warm) water.