The UK Government has said people should "stay local" and not travel unnecessarily, like driving to a park or beach for exercise.
The latest guidance issued on March 27 said that while it's important people exercise for their mental and physical health, people should only use open spaces close to their homes.
This means nobody should travel to open spaces that further afield, such as national parks.
The government has also warned that people should exercise outside alone or with members of your household.
However, gatherings of more than two in parks and other public spaces have been banned and police officers have the power to enforce this.
Watch: All you need to know about self-isolation
Dyfed Powys Police said on Saturday morning that officers at Storey Arms in Brecon Beacon were checking journeys were essential. Officers were ready to hand out £60 fines for non-essential travel, doubling on each subsequent offence.
On Twitter, the Brecon Roads Police unit said they had stopped a person from Bristol trying to climb Pen y Fan. They were told to go home immediately.
A spokesperson for the force said: "Travelling to our area from Cardiff, Bristol and Stroud to name some examples from today are not acceptable.
"We have to prevent a repeat of last weekend."
Meanwhile, North Wales Police reminded people that now was not the time to visit Wales' countryside and beaches.
South Wales Police's chief constable Matt Jukes said: "The majority of people are already making real sacrifices to save lives and we urge everyone to follow the advice that is designed to keep us all safe.
"We hope that the vast majority of our communities will recognise the need to follow the guidance and stay at home.
"South Wales Police has a track record of maintaining public order and safety in huge events and at times of emergency. We have always done so positively, with pride and professionalism.
"We will continue to do what we do best – engage with people. We will ask them to support their communities and stick to these important restrictions.
"As the public would expect, we will also utilise the new legislation when necessary where individuals show a total disregard for the restrictions which have been put in place to save lives.
"Police officers and other staff who you may speak to in the coming weeks are working to keep you and your families safe and well. They also have families to go home to."
The new, clearer advice comes after people were told to leave beauty spots such as the Peak District and local parks.
On Thursday, Derbyshire Police tweeted drone footage of walkers in the Peak District, drawing attention to what it said were unnecessary journeys.
Avon and Somerset Police said such non-essential travel included "driving to local beauty spots to do exercise" and its officers had given leaflets to visitors.
Meanwhile, Cumbria Police warned drivers would face fines if they visited the "closed" Lake District while North Yorkshire Police also told people to stay away from beauty spots.
The full guidance from the UK Government reads: