Nearly 60 per cent of readers who took part said Tory peer Seb Coe’s unwanted giant emblem should be placed away from the historic city centre.
The unpopular proposal to fix five aluminium Olympic rings to the Castle was dropped in the face of staunch public opposition.
The logo would have been unveiled on Hogmanay and remained in place until the end of next summer.
The decision to abandon the plan was an embarrassing U-turn for Historic Scotland, which along with the city council and the Scottish Government had recommended the Castle in the first place.
The Evening News selected five alternative sites and asked readers to vote on them.
Of 1000 readers polled, 34 per cent said the £200,000 logo should be hung from the airport terminal and 25 per cent voted for the Forth Bridge.
Just over a fifth said it would be acceptable to place the 30ft by 60ft rings on the Mound and only two per cent supported the Castle plan.
Deputy council leader Steve Cardownie, who oversees major events, had said that unveiling the symbol on Hogmanay would provide a spectacle for television cameras and a boost for tourism, but opposed it being in place for longer than a few days.
He said if the idea of displaying the logo in Edinburgh did go ahead, the Mound would be the most suitable.
He said: “The airport is a bit of a drab background because there’s nothing there and it does little to promote the city.
“Given the engineering history of the rail bridge that would be more iconic, although there might be costs associated with putting it up there.
“If the rings were placed flat on the Mound that would provide a panoramic view with the Castle as a backdrop.
“In terms of promoting the city, which is what I’m primarily focused on, that would provide a spectacle for television cameras to be beamed around the world and show Edinburgh at its best.
“But I think the organisers will have to marry up the views of the people and what will be suitable.”
A spokesman for Edinburgh Airport welcomed the findings and said it would discuss the plans with Olympic chiefs if they pursued the idea.
He added: “We’re flattered at being recognised by readers of the Evening News. Edinburgh Airport is the first impression many visitors have of the city and we’d be happy to discuss any way we could support the city and the Olympics.”
A spokeswoman for the Department of Culture, Media and Sport, which is delivering the Games, said: “We will continue to work closely with our partners in Scotland to support their celebrations of the 2012 Games and see if they want to propose another site.”