A nice option for a long day hike is to walk up all the way from the Akaroa tourist information center to the summit road above the town. If you are in reasonable shape, the walk shouldn't be too hard but it will take you the better part of the day to complete. Views of the Akaroa bay & the entire peninsula are superb. To start, simply walk eastwards from the town center uphill onto Balguerie st, then continue on Purple peak road until you reach the summit. You can go back the same way you came or opt for a longer walk down using one of the alternative routes that are found to the south. For more information and possibly a small map you can consult with the local tourist information center found in Akaroa.
APNP (Arthur's Pass National Park) offers loads of trekking options, some of the finest that NZ has to offer. Harper pass route, Three passes route and Cass-Lagoon track at the neighbouring Carigieburn Forest are only a few fine examples - but they are NOT for the novice trekker and should only be attempted if you have sufficient trekking and navigation skills. Don't leave out for these treks without a detailed topographic map as the markings in these treks are not of the standard that usually find in the more popular treks (many times, the best that you can hope for - is just a rock cairn of some sort). The most popular option is actually a day hike that takes you from the center of the village all the way up to Avalanche Peak. The complete journey up & down will take about 7 hours and it can be quite hefty if you haven't done much hiking so far (otherwise it's OK). There are two paths that go up: the Avalanche track and the Scotts track. The Scotts track is more moderate and has a more gradual incline but for the sake of your knees it is actually preferable to go up the steeper Avalanche track and go back down on the Scotts track. Things can certainly get 'sweaty' as you scramble your way up but once you go above the bushline, views are simply magnificant. If you haven't met Keas before (the local birds/parrots) - have this as a warning: do not leave your belongings alone as those birds are known to snatch and grab any personal item that is left by itself. They are suprisingly smart and agile!
One of NZ's most popular attractions, this national park is mostly known for its coastal track, although it contains other walking/trekking options as well, such as the inland track. Most people choose to stay around 1-2 days in the park, either by hiking it or canooing along the coastline. We opted for the 4 day track, going all the way north to Wainui. Some people choose to go back to the starting point after they finish hiking using a water-taxi. While it can be expensive, it is the fastest way to return. Hitching back from the northen edges of the park back to the park's entrance can be tricky as most hikers / visitors to the park usually concentrate along the more 'proximal' areas of the NP. In my opinion, you don't have to walk the entire track (like we did) in order to fully experience the scenery. If you're looking to socialize with other hikers and explore some nice glow-worms caves, the campsite and hut in Anchorage bay is your best bet, but if you're looking for a more relaxed, less crowded regions you should continue a little bit further north to Awaroa & Totaranui. Adjusting your expectaions is essential if you have a image of a secluded, desolate beaches when no footprint is visible. The park is packed with visitors in the high-season and even in the more remote parts of the track you are likely to see more than a few other fellow travellers. Despite that, Abel Tasman surley deserves at least 2 days of your time in my opinion. Pretty much everything you possibly need to know about Abel Tasman can be found here, in the DoC website: http://doc.govt.nz/parks-and-recreation/national-parks/abel-tasman/
Overlooked by some backpackers, but known among more 'serious' trekkers and locals, This national park offers several hiking & trekking options, ranging from a few hours to a full week haul in the mountains surrounding Lake Rotoroa & Lake Rotoiti.
You can find all the information you need regarding the area in the local DoC center, at the park entrance. Most overnighters either stay at the lake or climb via the Robert Ridge route / Speargrass track all the way to the Angelus Hut (which you need to book in advance with the DOC due its increasing popularity). However, if you are up to the task and you somewhat experienced with trekking - I strongly recommend to devote extra time and go for the full 5-7 days in the Travers Sabine Circuit. Although not an official 'Great Walk', it rivals with more famous tracks (Routeburn, Kepler etc.) in terms of scenery and natural landscapes. Aside from the Angelus hut, the track does not require any booking in advance. If you have DOC's Backcountry Hut Pass you can stay in the huts along the track for free. Best of all, you are not likely to find the crowds that flood the more popular tracks in Fiordland / Mt. Cook / Abel Tasman. The starting point for track is St. Arnaud. You should head out pretty early so you can continue upwards to the John Tait Hut.
On the 2nd day, its best to continue to the Upper Travers Hut and overnight there instead of attempting to cross over the Travers Saddle to the next hut. The Upper Travers Hut is located in a picturesque mountainside, below the saddle and is one of most memorable places I overnighted in New Zealand.
From there, on the 3rd day, continue over the Travers Saddle all the way to the West Sabine Hut, deep inside the bush. From this hut you can do an optional side trip to the Blue Lake Hut but you should know that this will longer your trek in about 2 days, since you will have to go back the same way you came. With or without doing this side-trip, the next stop will be at the sandfly-infested Sabine Hut, which is located next to the shores of lake Rotoroa.
From here you can continue through the Speargrass Hut back to St. Arnaud, but the real treat is go all the way up through the very strenous climb via the Mt. Cedric Route to the Angelus Hut. The views here are absloutely amazing and are worth the very long climb up. It is recommended that you stay overnight in the Angelus Hut but if you are very fit and you start very early, you can continue directly back to St. Arnaud via the Robert Ridge route (this day is going to very long and exhausting - so come prepared with plenty of water as there's isn't much of it until you reach Angelus Hut).
As always, the best source of information for detailed track notes, maps or weather forecast is the DoC itself, either in the national park's visitor center or the Doc's website (http://doc.govt.nz/parks-and-recreation/tracks-and-walks/nelson-tasman/nelson-lakes/travers-sabine-circuit/)