Help me find a 3-4 night tramp from Hokitika area?

Hey when are you planning on doing this trip? Whether there is snow on the tops and passes or not will potentially limit your options. The area inland from Hokitika has some great tracks but linking them into loops can sometimes take you into some really technical terrain quite quickly. I would suggest maybe trying to do a couple of smaller 2 day hikes in and out of a couple of different valleys like Cedar Flats and then up to Mt Brown Hut. Cedar Flats Hut is popular for the hot pools whereas Mt Brown has pretty amazing views out over the coast depending on what you’re looking for.

The track finder tool on this site offers many suggestions. Not knowing your capabilities I'm a bit reluctant to suggest a couple of loops from the Hokitika Gorge involving the Hokitika and Whitcombe, Mikonui and Doctors Creek. These loops traverse fabulous tops and quite rough country but are for the fit and experienced. As Airway Spies has suggested maybe do something from the Toaroha (Cedar Flats) roadend. Perhaps visit Cedar Flats and the hot spring nearby, then do a tops loop encorporating Adventure Bivvy, and Yeats Hut or Crystal Bivvy then return to Cedar Flat and go out the same way you came in. Or go from Cedar Flat Hut up to Pinnacle Bivvy in the Kokatahi via Adventure Ridge Bivvy and Zit Saddle then descend to the Kokatahi passing close to Boo Boo Hut and walk out to the road then do the shortish road walk back to your car. These trips have some challenges but are easier than the 3 or 4 nighters from the Hoki Gorge! FYI snow will not be a problem at the moment on any of these routes.

The West Coast is one of the most challenging areas in which to tramp. You mention you haven't been to NZ before, so I suggest being mindful of the difficulty of the terrain in the area. Below is a link from the DOC website for a trip in the area. It's described as 3-4 days and the huts and tracks are currently maintained by DOC. I've only been as far as Adventure Biv from the Toaroha side. Although it may be maintained, it ain't easy! https://www.doc.govt.nz/parks-and-recreation/places-to-go/west-coast/places/kokatahi-river-whitcombe-river-area/things-to-do/tracks/toaroha-zit-saddle-kokatahi-lathrop-saddle-styx-river-route/