Well as he's just introduced himself on the forum, I'm surprised Graham from Brewers Droop is not on here directing you to his bar. The Brewers Droop is a really good karaoke bar and not far from where you are staying.
If you turn left when you come out of your apartments and carry on along passing the Las Palmeras hotel on your right, the Full Monty, who have a karaoke slot also, further on past 3 restaurants, the last of which is I think called Daniels and then take a sharp right down a lane you will come to Brewers Droop, which is purely karaoke and has a really good system.
Its about 5 mins walk from your accommodation.
Personally, I only go to karaoke because my other half likes to sing, I don't really understand people going in to them if they are not singers themselves - there's loads of really good professional entertainment out there.
And Graham, if you do come on here - watch out we'll be in to see you in two weeks time when we are out again. If you don't know who we are - you will remember when the other half requests his new favourite song - Valerie by the Zutons!!!! I think we'll deserve a drink for making this recommendation!
C