Saheli Roy Choudhury
In Japan, the Nikkei 225 gained 0.14 percent to close at 20,874.06 while the Topix index slipped 0.05 percent to 1,582.13.
Australian shares retraced early losses as the country's benchmark ASX 200 rose 0.34 percent to close 6,026.1.
Still, the so-called Big Four banks in Australia stumbled followed gains in the previous session. Shares of ANZ were down 1.68 percent, Commonwealth Bank lost 1.36 percent, Westpac shed 1.24 percent and the National Australia Bank fell 1.4 percent. On Tuesday, banking stocks had gained after a special government-appointed inquiry into Australia's financial sector did not recommend breaking up any of the banks or interfering in the way they lend money.
The session in Asia followed gains on Wall Street overnight as other major markets in the region remained closed for public holidays.
In his State of the Union address, Trump claimed the only things that can stop a strong U.S. economy "are foolish wars, politics or ridiculous partisan investigations." He faces a slew of investigations from the new House Democratic majority and warned the party against coming probes into his policies and personal finances.
Trump also announced he will meet North Korean leader Kim Jong Un in Vietnam at the end of February as part of his administration's efforts to roll back the country's nuclear program.
Elsewhere, the Japanese yen, considered a safe-haven currency, traded at 109.75 to the dollar, weakening from levels near 108.5 last week.
The Australian dollar fetched $0.7145, dropping from an earlier session high of $0.7245. That followed after a speech from Reserve Bank of Australia Governor Philip Lowe revealed that the central bank is no longer as convinced that the next move in interest rates is likely to be up.
"The Bank believes it has room to be patient. Macroeconomic conditions remain broadly favourable — low unemployment and forecast above-trend growth," Ivan Colhoun, chief economist for markets at the National Australia Bank, wrote in an afternoon note.