If it's at Halloween, as I assume your half term is, you DEFINITELY have to go to Derry for that. It's become a massive thing, and the streets are full - it's really great.
Also Martin Crossan tours visiting the walls on foot is good: it was originally about the troubles and the history of the town in general but they'll tell you something about the Derry Girls etc as well as far as I recall - I've done it a couple of times when we've had foreign visitors and enjoyed it myself. It depends a bit on who your guide is but I couldn't tell you now which one is best: Martin himself has sadly died since he set it up.
Giant's Causeway - often a freezing day out IMO, even in summer, so in October??
OTOH check if the boat trips to see it from the sea are still going at that time of year: you're inside the boat so you're sheltered from the weather, and I found it great - though TBF as I've done the land version more times than I can remember, I don't feel the need to do the walks again: maybe for someone who's never set foot on it and is well wrapped up it might be worth a short time walking along the path.
And the visitors' centre too I guess.
I'm not from Belfast so maybe someone from there can give you more detail about to do, but Belfast is good too. The Titanic centre, obviously.
Music, you can find in Derry and Belfast, but I couldn't tell you which places offhand as it also depends what days you'd be visiting. Peadar O'Donnell's in Waterloo Street is probably the best-known one in Derry, but there are days where's no music there. Waterloo St has several actually: the Gweedore Bar, the Dungloe Bar, The Castle (just nearby, it's probably actually in Castle Street) or Badgers, in Orchard Street.
Here's a link here for music in Belfast: https://www.theirishroadtrip.com/live-music-belfast/
The Culturlann in Derry might be a good place to find out what's going on too.