The council said it was facing an unprecedented economic situation
Museums, public toilets and a council office could be closed under plans by Canterbury City Council to make savings of up to £3m in its 2010/11 budget.
The authority said it was facing significant pressures on its budget, including a fall in income. It wants to keep council tax rises to a minimum.
Plans being consulted on include closing six out of 40 public toilets and two museums.
The council's divisional office in Whitstable could be shut.
Council leader John Gilbey said: "We are facing an unprecedented economic situation that has required us to make some difficult decisions.
"Putting these suggestions forward is not something we are doing lightly, but it is a reflection of the financial position we are in."
He said the council had tried to protect frontline services, and make savings in providing discretionary services.
He also said the authority had considered closing leisure centres but had decided against it.
The proposed restructuring of the museum service would see a focus on the Museum of Canterbury and the Beaney Institute, but will lead to the closure of the Roman Museum and West Gate Towers Museum.
Herne Bay Museum would be turned into a community and education centre.
Grants to voluntary organisations would be cut by 3% and contributions to parish councils would be cut by 5%.
The council has put a full list of proposals on its website.