Mayor Karl Dean said Friday that with 83 percent of Davidson County checked, officials know 9,300 properties have been damaged, almost 2,000 of which are residences.
Dean said the cost of damages will go up because it doesn't include roads, bridges or buildings' contents.
"While the numbers seem daunting, and they truly are large, Nashville is in the process of recovering," Dean said.
Singing the Blues at Grand Ole Opry
The death toll from last weekend's storms and flooding, in Tennessee, Mississippi and Kentucky, climbed to 31 with the discovery of a missing kayaker's body in Kentucky. Twenty died in Tennessee alone.
The National Weather Service said the Cumberland River crested this week at its highest level in Nashville since 1937 - 51.86 feet on Tuesday evening - following 13.5 inches of rain that fell over two days The flood stage is 40 feet.
The all-time record is 56.2 feet in 1927.
Homeland Security Secretary Janet Napolitano planned to tour the area Saturday.
Four water-damaged schools - Pegram and Kingston Springs Elementary Schools, Harpeth Middle and Harpeth High - will not reopen this year. County school district officials announced that the students will be waived for the remainder of the school year, which was to end May 26.
Other schools will reopen Wednesday.
More than 12,000 Tennesseans had registered with the Federal Emergency Management Agency for disaster assistance by midmorning Friday, with 250 inspections complete, and the agency had already approved $1.5 million in individual assistance.
Already some residents are seeing significant progress, thanks to kind strangers. Kristin Griffith, of nearby Franklin, saw 10 people she didn't know ripping waterlogged boards off her floor at one point.
Adam Johnston had bags of lime stacked up outside his house to dull the smell once he and other volunteers clean out the 4 inches of sewage and sludge swept under his house by the flooded Harpeth River.
Johnston's two daughters, 5 and 3, are staying with his in-laws. His forearms and legs are nearly raw from climbing through the sludge, and he said his tetanus shot was a must. Still, he is optimistic about fixing the home where his family moved only nine months ago.
"We're looking at it as just a forced renovation," he said.
Help is also coming from the gridiron. The owner of the Tennessee Titans has joined with the NFL and the NFL Players Association in giving $400,000 to the American Red Cross and a Tennessee group to help the state recover.
Owner Bud Adams decided to donate $200,000 from his Titans Foundation and encouraged the league and the players union to match his gift.
The money will be split between the Red Cross and the Community Foundation of Middle Tennessee, which also runs the Metro Nashville Disaster Relief Fund and the Tennessee Emergency Relief Fund.
Adams also promised that Titans players and staff will be out in Nashville next week to help with recovery.
CBS Affiliate WTVF reports five disaster centers will remain open this weekend for flood victims; 130 people are staying at three shelters. Food boxes and meals have been distributed at the centers.
Cases of bottled water are also being made available, and can be picked up at several locations around Nashville.
In Kentucky, the commanding general of the 101st Airborne Division at Fort Campbell is giving his soldiers a day off to clean up their homes and help others after severe flooding in Tennessee and Kentucky.
Campbell said in a news release he was also encouraging those who had no damage to volunteer in recovery efforts on Friday.
Nashville Under Water