Check out this website for info, it will have the majority of the fishing spots you’ll be going past, also try and get a look at a few of the fish and game pamphlets they have them in almost every fishing tackle shop. Around Queenstown you have all the little lakes around Lake Wakatipu within a short distance, Lake Moke, Kirkpatrick, Hayes, all offer good fishing with Lake Hayes maybe not having such as good access due to all the willows. In Wanaka you have the lake itself which if you can find a nice secluded bay has plenty of nice trout to keep you occupied. Then theres the Upper Clutha which has a lot of trout in it. West Coast has a tonne of rivers and lakes and almost all hold good numbers of browns check out the website above to look at which ones you’ll be going past.
Streamers:Woolly Buggers, rabbit patterns.
Dries: Elk caddis, mayfly dries, emergers, blowfly humpies, cicada, royal wulfs, parachute adams.
Nymphs: Hair and copper, pheasant tail, any generalistic nymph, from unweighted through to heavy tungsten.
Long leaders typical would be 16-17 feet but go longer if the waters particularly clear and fish a bit shy (which is often the case)