The Welsh Local Government Association also wants food outlets to be banned from being within 400m of schools.
These proposals are part of its manifesto for the next Welsh government.
A budget shortfall of Â£941m for councils by 2020 has been predicted by the WLGA.
As part of its proposals, the organisation said proceeds of the 5p levy on plastic bags should be spent on front-line services, raising up to Â£22m.
It also wants responsibility for public health services to be given to Welsh councils, as has happened in England.
A preventative care fund, paid for by money owed to the Welsh government as part of a UK government commitment to increase spending on the English NHS, should be set up to pay for services aimed at keeping people healthy and out of hospital, it has said.
WLGA leader Bob Wellington said: "As local government leaders we make it clear that the current approach for funding and running public services in Wales is clearly not working and that the next Welsh government must free up and trust local government to work with its communities to deliver a better solution."
As well as scrapping the Â£60 a week cap on how much councils can charge for non-residential care, it wants an end to to protected school budgets.
Amid ministers' plans to cut the number of local authorities from 22 to single figures, the WLGA has also called for "clarity" from the Welsh government about council merger plans.
More power and freedom on how cash is spent should be given to local councils, the body representing them has said.