Clinton later told reporters that Washington would seek Jakarta's "advice and counsel" on how to engage the Muslim world, Asia and beyond.
She said Indonesia, as a thriving democracy and Southeast Asia's largest economy, was an obvious inclusion on her four-nation tour of Asia.
Indonesia is also Clinton's first trip to a Muslim majority country since Barack Obama, the US president, promised to heal the rifts created with the Muslim world under his predecessor.
"When the United States is absent, people believe we are not interested and that creates a vacuum that destructive forces can fill"
Hillary Clinton, US secretary of state
"Of course the personal relationship that President Obama has to Indonesia is very important to him," Clinton told reporters after meeting Yudhoyono.
Obama, known to his childhood friends as Barry, attended primary school in the upmarket Menteng area of central Jakarta, the Indonesian capital, from 1967 to 1971, after his American mother divorced his Kenyan father and married an Indonesian.
"I decided I wanted to come to Asia on my first trip because we concluded in the last several years we hadn't paid enough attention to many parts of Asia.
"Our interests aren't just focused on China," she said, adding that "when the United States is absent, people believe we are not interested – that creates a vacuum that destructive forces can fill".
Clinton got an icy reception on Wednesday with a few hundred protesters shouting slogans and throwing shoes at a caricature of her.
|Clinton visited a US-funded project in a
Jakarta slum on Thursdy [EPA]
Later on Thursday, however, crowds gave the US diplomat a rousing welcome as she visited US aided projects in a slum in central Jakarta.
She told a group of craftswomen that she was "proud" of their work, and patted children on the head.
On Wednesday Clinton said the two countries intended to co-operate in areas ranging from security and counter-terrorism to climate change.
Clinton heads to South Korea later on Thursday before wrapping up her trip with a stop in China later in the week.
Her visit to Seoul comes as tensions mount between South and North Korea, with Pyongyang saying on Thursday that it was ready for war and repeatedly threatening in recent weeks to reduce the South to ashes.
Pyongyang is thought to be readying its longest-range missile for launch in what analysts say is a bid to grab the new US administration's attention and press Lee Myung-bak, South Korea's president, to soften his hardline stance against it.
Speaking in Tokyo on Tuesday as she began her first foreign trip since taking office, Clinton said that a North Korean missile launch would be "very unhelpful".