@hildazelda it's a lovely wee city and great to see in a few days!!
I'd recommend as others have Titanic museum, the bus tours of the city or a walking tour (there's a lovely foodie walking tour). Also the Folk and Transport museum the Ulster Museum (free entry) and St George's Market.
I actually would highly recommend the black cab tours as to say you need a "neutral" in Belfast, given its history, is crazy. That doesn't mean that you can't have an amazing tour whilst getting to understand the perspectives of an individual who has lived through it. Doesn't matter which "side" you come from, the whole point of tour is to get a perspective from someone who lived through it.
HMS Caroline, and Nomadic also speak to the city's ship building past.
I'd recommend a walk across Divis/Black Mountain (National Trust) or along the top of Cavehill to see the view from "Napoleon's nose" to see the views of the city and lough in all their glory. So beautiful. The Ridge walk is beautiful (we met visitors from Chester there just yesterday!)
So many restaurants and bar options I can't even keep up! We are a foodie city, we overfeed everyone😂.
Belfast Castle is a great spot and the walks around it beautiful. Queen's University well worth seeing.
For wet weather a great day out is W5, the science museum in the Odyssey centre. You can do a full day here easily with in and out exit for lunch possible.
Further afield from Belfast there is of course the Giants Causeway. Or in the other direction Slieve Gullion and its fairy ring and playpark is pretty special. Our kids adore it!!!! All of the National Trust properties are great if you have longer time to spend.
The Grand Central Hotel has just opened as one of our tallest spots and I'm told their cocktails in their top floor bar are great, if incredibly expensive!!! View from "the dome" in Victoria Square shopping centre is fabulous and free!
Check out "what's on NI" for details of what's going on.
St Anne's cathedral is beautiful. You can tour the City Hall also. There are plenty of great hotels around the place.
Lisburn Road is nice for a wander and some shopping as is Newtownards road. As well as our great city centre, that has just had a rough time with a fire in a major listed building.
We are a beautiful city of friendly people and well worth a weekend. As Lonely Planet agrees. To those who say we're dirty, grey and drab.... Huh????!!!!! You need to open your eyes!!! Every city has a back end. Most aren't blessed to have a mountain, a city and a lough with stunning views and great people. You'll have a lovely weekend. X