Closing the Museum of Nottingham Life to general visitors would be a mistake, Nottingham's Civic Society has said.
Visits to the attraction would be reduced to just groups and schools under the city council's budget proposals, saving £40,000 a year.
The authority said that tough decisions had to be made as it bids to save £20m from its budget for 2012/13.
Ian Wells, from the civic society, said authorities needed to be responsible for the heritage on their doorstep.
"It is very sad and very short-sighted," he said.
The Museum of Nottingham Life, housed within five 17th Century cottages at Brewhouse Yard, depicts the social history of the city over the last 300 years.
It contains reconstructed 1920s shops and a Victorian school room.
"They have really made the past attractive there at a time when we have a great interest," Mr Wells said.
"We accept that cuts have got to be made but it always seems one particular area that seems to be hit."
Presenting its budget proposals for 2012/13 to its executive board on Tuesday, Nottingham City Council said its priority was to support jobs and the local economy and protect services for vulnerable people.
As well as changes to the city museum's opening times, the authority announced plans to cut 195 council jobs and the closure of the Marlestones elderly persons care home in Bulwell.