Depends how near and how easy-moderate :-)
Orongorongo valley - about 40min drive through Wainuiomata, then a couple of hours easy walk into a pretty river. Have lunch then walk back out. There are various bush tracks in that area too. Could camp the night too or they have bookable huts.
Kapakapanui Hut - Near Waikanae, then a fairly cruisy overnight tramp with a night at a public hut. Its a muddy bush track but well marked. Walk all uphill one day and all down the next.
Kaitoke - North of Upper Hutt but before Rimutaka Hill there are good bush walks, and a nice overnight tramp would be to pop over Puffer Saddle and camp near Smiths Creek shelter in the Taherinikau valley.
If you want to drive further than that then there is no end of good trips in the Tararuas either accessed from the Kapiti-Horowhenua or Wairarapa....
Richie