Ok, I'll stick with the immediate area. Bars/pubs right by you - Smugglers and Comics. No karaoke though. Drunken Duck - if they're still doing it - would be closest; it's by the Condes de Alcudia Hotel, a few minutes walk away.
There aren't that many bars in the harbour area. It's more restaurants. But evenings there is often entertainment on the promenade and there is a market every evening in the marina.
Sounds like you might want to get a bus or taxi to the so-called Bellevue area for the odd evening. You can walk, but it's about 20-25 minutes. Loads of places there that do all sort of entertainment.
Also, check out the old town of Alcudia. Very different to the rest of Alcudia. You can walk from the Alcudia Hotel - about 10 minutes. Not a lot to do as such, but there are regular evening events like the Via Fora (son et lumiere) by the city walls.
Does this help?