Free parking will be available from 10am each day for up to four hours.
But businesses feared the plan would affect trade by reducing the number of free parking places.
Some councils, including Newport and Wrexham, have already tried free parking initiatives to encourage shoppers.
Other places on the hybrid free parking list include New Haven, Connecticut, Fresno, California, and Albuquerque, New Mexico.
Wiltshire Council also agreed to allow it to add 700 free parking spaces.
There has also been free parking at council-run car parks after 17:00 GMT.
Transport Minister Norman Baker said: "Motorists who pretend to be disabled to get some free parking are frankly disgraceful".
Further plans include a maximum increase in council tax and an end to free parking at park and rides.
The three car parks are in Station Road, Link Road and Clevedon Road and offer three hours of free parking.
BBC: Nailsea Town Council wants to keep free parking in town
Meanwhile, neighbouring Carmarthenshire council is to offer free parking from Boxing Day to New Year's Day, but not before Christmas.
BBC: Free parking in Pembrokeshire to boost Christmas shopping
He added that pay machines would not accept money during the free parking days and that there would be increased signage.
"We'll tie it in with the hotels, " he said, "and we'll give them free parking and landing fees at the airport".
While no other major airport offers such a generous incentive, several cities offer free parking for electric cars in metered spaces.
WSJ: It's Less Easy Being 'Green' as Los Angeles Yanks Plug on Free Parking for Electric Cars
It said the new store would improve pedestrian links between the Bridgwater Canal and the town centre, and provide extra free parking.
Permits giving about 1, 300 Torbay Council staff free parking have been criticised.
Free parking on Sundays and weekday evenings in Leeds could be scrapped.
An Oxfordshire authority is to provide free parking over the Christmas period.
On offer to commuters during Wednesday's Car Free Day have been free parking on the outskirts of the city and a free bike loan scheme.
BBC: NEWS | UK | Scotland | Highlands and Islands | City car free day gets into gear
More than 200 Cornwall Council staff and elected councillors have special passes which allow them free parking in council-owned car parks, BBC Cornwall has learned.
According to Ms Wood, many town centres across Wales were unable to compete with the attractions of the large retail parks that were offering free parking to customers.
Out-of-town shopping centres are suburban because they offer "the city without the scary bits", she says, like free parking, no Big Issue sellers and no graffiti.
Maureen Hinton, a retail analyst at Verdict Research, said out-of-town shopping centres with free parking and a wide range of stores gave consumers what they wanted.
Now, one quarter of the hotel's rooms are occupied by business travellers - thanks in part to free parking, complimentary breakfast, wireless internet and the hotel's 24-hour business centre.
As a sufferer himself, he is also a driver with a blue badge but that does not entitle him to free parking in his local area, Caerphilly.
Don't be lulled by the folksy tales of pimento cheese sandwiches and free parking: The Masters is a thoroughly modern, high-tech, sponsorship-soaked event, eager to wield its influence.
John O'Roarke, managing director at LV, said the lack of free parking in council areas was "putting increasing pressure on cash-strapped motorists", with many "resorting to parking illegally".
Les Byard, manager of St Tydfils shopping Centre in Merthyr Tydfil and also chair of the town's business club, told BBC Radio Wales that free parking would be ideal.
He said members of the public were subsidising free parking for councillors and council staff and the party had proposed to introduce a charge for parking permits for council premises.
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