As stated before, I'm fairly sure the Warriors are locked into a fairly good agreement with Mt Smart Stadium. I don't think its pure choice that they don't travel, given in 2002 they marketed themselves as the New Zealand Warriors in a very good media campaign on both sides of the Tasman.
League definitely registers in the South. The West Coast (albeit a very small population) and Canterbury in particular have good league backgrounds. There's been a fair few Kiwis over the past decade or so from the South Island: Quentin Pongia, Simon Mannering, Whetu Taewa, the coach Frank Endacott was from Canterbury, Setamaita Sa, Lewis Brown is in the squad, Jeremy Smith, Dene Halatau, David Vaeleki, David Kidwell, Terry Hermansonn, Brent Stuart, Simon Angell, Aaron Whittaker...
In terms of Wellington born and/or bred players: Stephen Kearney, David Faiumu, Sika Manu, Paul Whatuira, Paul Rauhihi, Marc Ellis, John Lomax, David Lomax...
In terms of non Auckland/Wellington/South Island, you still have the likes of Hohaia, Koopu, Grant Young, Willie Talau, John Timu...