Assuming you are inside of the city proper, just stay in whatever hotel that has a MRT station nearby. It's nothing like our shitty skytrain. If you are bling... XingYi district is a good bet. I personally prefer near the Taipei main station, but that's more to do with my F&F.
And the MRT would take care of most of the transportation. Oh, and get a card for the MRT, you can load money onto it and use them in convenience stores like 7-11. And yes, they are everywhere. Last thing, get a taxi. They are pennies comparing to what we spend here and they are everywhere inside of Taipei; most of A-B trip inside Taipei city would run you less than $10CAD.
Regular KTV=Cashbox or Holiday. Cashbox is more on the higher class side while Holiday is for younger audience.
Club... coming from Vancouver club scene, any club worth mentioning in Taipei would blow your mind.
No strip joint per se, but if something "fun"
is in the plan, I'd suggest to check with a local guide (it's actually easy when you hit the clubs) so you are actually getting your money well spent and have some fun.
Food, depends on what you are into. Taipei food would generally be ok and above, but nothing amazing IMHO. (yes, I'm picky).