Fresh off a trip to Spain, the pair also stopped with family and friends for lunch at the Boatyard Bar and Grill in Eastport.
Dick Franyo, the restaurant's owner, said U.S. Secret Service agents came in about 45 minutes before the lunch. The first lady ordered crab cakes and "loved them," he said.
Franyo, who is vacationing in Montana, praised his staff for handling the visit and said it is "the biggest thing that ever happened to us."
"We are honored," he said.
Tammy Reece, general manager of the restaurant, said the venue had been "highly recommended" by Obama's staff.
"They had definitely scoped it out," she said.
Gov. Martin O'Malley greeted Obama, Sasha and others around 11:45 a.m. before they took a private tour of the building, said Shaun Adamec, a spokesman for the governor.
Adamec said the hourlong tour was an "educational summer visit" and O'Malley gave pewter pillboxes engraved with the state seal as gifts.
Dr. Edward Papenfuse, the state archivist, took the party on a tour that included the building's historic rooms, the governor's office and Lawyers Mall.
"It was very enjoyable," Papenfuse said. "We talked about the early history of the State House."
House Speaker Michael E. Busch, D-Annapolis, also talked to the visitors about the House chamber.
"She was as gracious as could be," Busch said. "She was as down-to-earth as anyone you would want to meet."
Papenfuse also showed the group the state's original version of the speech, delivered in 1783 in the old Senate chamber, in which George Washington resigned as head of the Continental Army, a key moment in America's tradition of maintaining civilian authority.
"That's what made Sasha's dad (President Barack Obama) the commander in chief," he said.
Papenfuse said the first lady was also given an autographed copy of Alex Haley's book, "Roots." Haley was inspired to write the book after he found a Maryland Gazette advertisement about a slave ship that brought his ancestor, Kunta Kinte, to Annapolis in 1767.
One landmark left off the tour, however, was the State House's dome - because of high temperatures.
"It was way too hot today," Papenfuse said.
County Executive John R. Leopold said he met Obama and her companions at the Naval Academy and discussed everything from the county's efforts to curb childhood obesity to the likelihood he knocked on President Obama's door when he was involved in Hawaii politics.
"It was a great opportunity," he said.
The Associated Press contributed to this story.