"Two doses of 70 per cent vaccination [is the target] and NSW, if we had the current pace, we will hit that around the end of October," the premier said on Wednesday.

But life won't be "back to normal" until 80 per cent of the population is vaccinated towards the end of the November, the premier said, referencing the Doherty Institute modelling produced for the national cabinet.

NSW reported 344 new locally acquired cases of COVID-19 in the 24 hours to 8pm on Tuesday.

On the second worst day of the eight-week outbreak, at least 101 of the new cases were circulating in the community for all or part of their infectious period.

Another two people have died - a man in his 30s with underlying health conditions from Sydney's northern beaches and a man in his 90s, taking the number of COVID-related deaths in the outbreak to 34.

Both men were unvaccinated.

There were 106,592 vaccination doses administered in NSW the 24 hours to 8pm on Tuesday night, taking the number to have received a first dose to 46.20 per cent.

Ms Berejiklian said some people in NSW might be allowed more freedoms if six million vaccinations - or roughly 50 per cent having a first dose - were administered by the end of August.

"That is what we are working towards and something that our government is very keen to make possible," she said.

A Sydney man who prompted the Byron Bay lockdown when he travelled to the region while symptomatic has been served a court attendance notice at Lismore Base Hospital.

The 52-year-old man from Rose Bay will be charged, having travelled to Byron Bay with his two children without a "reasonable excuse" and in contravention of the public health orders, police said.

He will appear in Lismore Local Court on September 13.

Ms Berejiklian pleaded with the public to stick to the rules.

"It is just a handful of people doing the wrong thing that really causes grief for everybody," she said.

The Dubbo local government area in the state's central west went into a seven-day lockdown on Wednesday after two positive cases were recorded in the region, prompting panic buying in the town.

The Department of Education was advised by NSW Health late on Tuesday of a case at Dubbo West Public School.

The school has been closed, while staff and students are being asked to isolate and get tested if they have symptoms. The positive case has also been linked to Macquarie Anglican Grammar School and nine close contacts have been identified and are in isolation.

Late on Wednesday eight local government areas in western NSW were also placed into lockdown after a COVID-19 case was detected in Walgett.

Stay-at-home orders will apply to Bogan, Bourke, Brewarrina, Coonamble, Gilgandra, Narromine, Walgett and Warren LGAs, from 7pm for one week.

More than six million people in Sydney and surrounds are now in lockdown until at least August 28, with the Hunter, Byron Bay, Armidale and Tamworth areas also enduring lockdowns.

There were no extra cases in Armidale, Tamworth or the Northern Rivers region but it's unlikely the Hunter region will come out of lockdown on Thursday after 14 new cases were recorded overnight.

Meanwhile, Bathurst Correctional Centre is the first NSW prison this year to record a COVID-19 infection and has been locked down as a precautionary measure.

The 27-year-old man arrived on Saturday and was released on bail on Monday.

Fennel Bay Public School at Lake Macquarie, near Newcastle is also closed on Wednesday after a student tested positive to COVID and Ryde Secondary College in Sydney's west is also closed after a member of the school community tested positive.

There are 374 coronavirus patients in hospital, 62 of them in intensive care and 29 are ventilated.

Chief Health Officer Kerry Chant said none of the people in intensive care had received two doses of the vaccine.

"You can see that the vaccine works," Dr Chant said.

There were 119,256 COVID-19 tests reported to 8pm on Tuesday night.

Australian Associated Press