Price has been staying at the venue since her alcohol-fuelled car crash last month.
Price was told to have treatment at the Priory after pleading guilty to drink driving while disqualified and without insurance.
On Friday, Price was spotted wearing pink tracksuit bottoms and a white hoodie as she shopped and then had a spray tan. Sources told The Sun she was buying things for her mother’s birthday.
Last month, Price appeared at Crawley Magistrates’ Court after she crashed her car near her home in Sussex.
She was told to have treatment at the Priory after pleading guilty to drink driving while disqualified and without insurance.
She was told that her sentence would be deferred on the condition she goes to the renowned centre and does not commit any further offences.
She is banned from driving in the interim.
Chair of the bench Julie Hutton warned her: “We regularly send people to prison for driving whilst disqualified.”
The mum-of-five was told she must also engage with the probation service so a report can be prepared.
“On that basis, Ms Price, you are free to go and good luck at the Priory,” Ms Hutton said.
Defence solicitor Joe Harrington said Ms Price was going through a “really difficult period” after a lot of “personal problems”.
He said: “She has had a lot of personal problems recently.
Currently she is in the process of bankruptcy proceedings, so her house may be repossessed.
“So, quite a lot going on in this lady’s life, a really difficult period.”
Crawley Magistrates’ Court heard she reportedly told police officers at the scene, “I took drugs, I should not be driving, I admit it all.”
A drugs wipe gave a positive reading for cocaine, prosecutor Debbie Jones told the court.
Earlier, her family said they have been concerned “for some time” about the TV personality’s mental wellbeing.