Rotorua is a city in the North Island of New Zealand.
West towards Auckland, Hamilton (New Zealand)
Take bus 01 from the city centre towards Ngongotaha and get off at "Ngongotaha Road - Opposite No.430", which is shortly before the roundabout of State Hwy 5 and Ngongotaha Rd. Cross the roundabout area and walk westwards on the left hand side of the State Hwy; a few metres past the speed signs, the shoulder becomes very wide – a perfect place for people to stop before speeding up, and most cars will be going all the way to Hamilton or even Auckland.
North towards Tauranga (via SH36/Pyes Pa Rd)
This route is slightly more scenic than the Eastern approach to Tauranga (since you'll pass through Kaharoa Gorge) and is recommended if you're heading for Tauranga CBD or the city's western suburbs.
Take bus 01 from the city centre towards Ngongotaha and get off at "Waiteti Road - Fronting No.41", which is directly opposite a marae (a traditional communal gathering place, often a beautiful wooden building, of the Māori people). Walk back to the main road, carefully cross it, turn right and walk up for a few metres. Shortly before the "speed limit ends" signs, the shoulder is wide enough for someone to stop, and vehicles are not at their top speed yet. This is your hitching spot; although some people's destination will be Hamurana (a locality on the northern shore of Lake Rotorua), most will be going straight to Tauranga.
East towards Whakatane, Gisborne and Tauranga (via SH33)
This route is a smoother ride than the Northern approach to Tauranga (due to the fewer bends and sharp turns on the road) and is recommended if you're heading for Mt Maunganui, Papamoa or the city's other eastern suburbs.
Take bus 10 from the city centre towards Rotorua Airport and get off at the airport. Walk back to the main road and hitch straight from the intersection, where the shoulder has been widened for bicyclists (which are a rare sight, even in summer). If you have no luck, you can walk up the road towards the city boundary: Just before the "speed limit ends" signs, there's a sealed half circle for cars to do a u-turn, where people can stop to pick you up.
Alternatively, take the same bus but get off at "Vaughan Road - Fronting No.36A". Walk back, turn left and head for the big roundabout. Once there, turn left and hitch from the former bus stop just in front of Repco. Be aware that the majority of the (heavy) traffic during the day here is local and doesn't leave the city.
South towards Taupo, New Plymouth and Wellington
If you're feeling lazy, you can almost hitch from the CBD: There's a bus stop/bay on Fenton St adjacent to the Pak 'N Save supermarket where you could stand and put out your thumb. There's also plenty of opportunity further down on Fenton St since the speed limit is 50 km/h and the shoulder is wide enough for people to stop (often, there will be parked cars/trucks though).
To maximise your chances however, take bus 11 from the centre towards Toi Ohomai Institute of Technology via Fenton Park and Te Puia and get off at "Hemo Road - Fronting No. 30", which is directly in front of the Te Puia tourist attraction. You can also walk there if it's a nice day, it'll take roughly 45 minutes from the CBD. Hitch a few metres up from the bus stop (so as to not block the next bus if you happen to be still waiting); the shoulder is long and wide here, and most traffic passing this bus stop is leaving town.