The Centre for Cities has urged whoever is elected on May 6 to introduce the potentially controversial measures, which would reduce demand for car travel into major urban centres and increase demand for public transport.
Its report setting out policy priorities for the metro mayor also says they should follow the example of Greater Manchester's Andy Burnham by taking local bus services into public control.
And it says revenues raised by these measures should then be used by the mayor to support an expansion of public transport in West Yorkshire and to pay for the county's long-awaited mass transit system.
Transport is likely to be one of the key issues for the candidates for West Yorkshire mayor, despite the pandemic resulting in huge falls in the number of journeys made around the county.
The report says poor air quality and congestion are both problems across West Yorkshire and that "congestion is a particular problem in Leeds with the city having one of the most congested roads outside of London".
It says that a congestion charge, a free levied on most motor vehicles driven in a certain area, reduced traffic in London by 21 per cent.
And a workplace parking levy in Nottingham, a charge made by the council on employers for the number of parking spaces provided for employees, reduced congestion and pollution.
Elsewhere, the Centre for Cities says the mayor should target support for adult education in areas where it is most needed and use their influence to shine a spotlight on underperformance in education.
It says West Yorkshire makes a significant contribution to the national economy of more than £55 billion a year but productivity sits below the national average, which is in part a result of challenges around education and skills.
In Bradford and Wakefield in particular, the key issue is the lack of skills among workers and poor GCSE performance.
To support city centres, the think-tank says whoever is elected should "encourage people back into Leeds city centre when it is safe to do so" after the pandemic.
And it says the mayor should allow growth in Leeds through creating more high-quality office space and replace industrial and retail space with high-quality office space elsewhere in West Yorkshire.
The report says: "The election of a mayor will provide two main things for West Yorkshire. The first is extra powers and budgets to help support future growth of the economy.
"And the second is the role of advocate for the area in dealings with both national government and potential international investors.
"A number of other city regions, most notably Greater Manchester, have benefited from this for a number of years now. May’s election provides the opportunity for West Yorkshire to catch up."
The mayoral role was created as part of a devolution deal signed last March which will allow the area to unlock £1.8 billion of long-term funding alongside greater powers on adult education and skills, transport, housing, and finance.
In the running on May 6 are Tracy Brabin (Labour), Matt Robinson (Conservative), Stewart Golton (Liberal Democrats), Andrew Cooper (Green Party), Bob Buxton (Yorkshire Party), Wajid Ali (Reform UK) and Therese Hirst (English Democrats).