The authority will freeze council tax next year, but will cut 300 jobs and many services to balance the books.
They include closing Splott pool, selling Flat Holm Island in the Bristol Channel and ending the Big Weekend event.
There will be more money for schools and social services.
The Labour-led cabinet said cuts of £22m had to be found in the next budget and it needed to find £110m of savings during the lifetime of the current council.
It outlined some of its proposals in a full council meeting on Thursday evening.
Russell Goodway, who holds the finance portfolio in the Cardiff cabinet, told colleagues: The picture is far from rosy. I am not looking to put a gloss on it or spin. There is no escaping the pain."
Delivering proposals for the 2013-2014 budget, he said some service areas will see budgets cut by 90% by 2021.
He added that there would be "serious collateral damage", with jobs hit - including 300 post closures in the next year.
Savings that will be made include:
Mr Goodway said that the council did not intend to close the city's riding school, which had been feared.
Instead, it was working to find an alternative operator to run the riding school on its 30-acre site in Pontcanna.
Staff at the riding centre - who protested outside the meeting - claimed they were sent letters telling them that the school would close on 1 April.
But Mr Goodway told councillors that the school would remain open until a new partner was found.
He also said that there would be an increase in spending for schools - but it would mean they would have to buy some of the services the authority currently provides for them.
Social services would also get an increase in their total budget, he added.
The council did have the option of increasing council tax to bring in more money, but Labour in Cardiff pledged to freeze council tax during last year's elections.
Both Conservative and Liberal Democrat opposition councillors said they would wait to see "the devil in the detail" before coming to any firm decisions on the budget proposals.
But the Plaid Cymru group leader, Neil McEvoy, said the proposals were being delivered by a "right-wing Labour council" who were nothing more than "red Tories".
The budget will be put to a full council meeting at the end of February.
A swimming pool will be closed, school music subsidies stopped, library hours cut and even an island sold under plans to save Cardiff council £110m.