Auckland to Hamilton is less than two hours driving, especially from the airport, as that's way at the south side of Auckland. Not much to see en route either (erm, a themepark and shopping malls in Manukau city, and then pretty much emptiness until Hamilton, as I recall it).
What I might suggest - if you're a LotR fan - is to drive two hours to Matamata instead (east of Hamilton), and do the Hobbiton tour from there (the only option for you that day leaves at 15:45 from the visitor information center, or at 16:05 from right near the entrance.
There's some nice homestays in Matamata, or otherwise it's then a further hour to drive from Matamata to Hamilton (no convenient highways there; it's only 60km otherwise), so it's not exactly ideal. (Maybe better to do it the next day, en route to Rotorua.)
The most worthwhile place that's really en route then is actually Hamilton itself. It's not a city which is known for drawing the tourist crowds, but they have some nice gardens (especially since it's effectively spring), and it's pleasant enough to just wander around the city center.
[ Edit: Edited on Sep 5, 2008, at 10:29 AM by Sander ]