....Just Kidding, we aren't that mean down here

As Blazer said, Kapiti is a great place to hit with that Stealth, nice beach to launch off but be weary of the strong currents out there - maybe tag along with someone if you can. Where in Welly will you be based? Most people use dead baits but soft baiting has grown a little in the last few years here and certainly worth trying if that's what you're use to. I have witnessed plenty of decent fish being caught on softies and slow jigs etc.
Harbour/Makara/Pukerua all provide fishing opportunities with the West generally being better, but still people get great catches in the harbour. Probably a bit rocky-er terrain to launch off than what you are use to so may need to watch that with the Stealth.
I don't think about the tides (incoming/outgoing) too much as you will find spots that work for each tide. On strong tides through it can be honking through quite quick so be careful if not use to that especially if you are anchoring in it.
If you are on Facebook, have a search for 'Wellington Kayak Fishing Community' page as people probably see that more than here - chuck up a post when you're down if you want to tag along with someone and i'm sure someone will be glad to ehad out with you.