As promotions for Last Fantasy and its main single "You & I" continued into 2012 in South Korea, IU began preparations for her debut in Japan by playing two shows at the Bunkamura Orchard Hall in Shibuya, Tokyo to an audience of about 4,000 people on January 24, 2012. Subsequent to the concert, both "Good Day" and "You & I" were released as new singles in Japan with translated lyrics to moderate success. According to Japan's Oricon Singles Chart, the single album of Good Day sold 21,000 physical copies on the first week of release with the single debuting on the chart at number six. On the Billboard Japan Hot 100, "Good Day" peaked at number 5. "You & I" peaked at number four on the Oricon Singles Chart and number eleven on the Billboard Japan Hot 100. In support of her Japanese single releases, IU toured five cities—Tokyo, Sapporo, Nagoya, Osaka and Fukuoka—in a mini-concert series called IU Friendship Showcase - Spring 2012.

IU embarked on her first concert tour, Real Fantasy, in June 2012. She played shows in six different cities across South Korea, starting with two shows in Seoul. The opening shows on June 2–3 were sold out within 30 minutes of the tickets going on sale on April 17. It was reported that 43.8% of ticket purchasers were between the ages of 20 and 29, while 71% were male, which was considered uncommon for a K-pop concert. The tour continued to Ulsan, Jeonju, Suwon, Busan and Daegu, before returning to Seoul with two encore concerts that ended on September 23, 2012. Guest performers included Ra.D, Lim Seul-ong and Lee Seung-gi.

Due to her commitments towards preparing for her first solo tour, IU was unable to make broadcast promotions for her fifth Korean extended play, Spring of a Twenty Year Old, which was released on May 11, 2012. The album, named to celebrate IU turning the Korean age of 20, contains three songs with the lead single being "Peach". Self-composed by IU, "Peach" peaked at number two on the Gaon Digital Chart and number three on the Billboard K-pop Hot 100. The second single released from the album was "Every End of the Day" (하루 끝), which topped the Gaon Digital Chart for two weeks and the Billboard K-pop Hot 100 for four weeks. In place of the usual 4–5 minute music video that usually accompanies a single release, a 26-minute-long documentary-style music film was shot in Venice and Burano and released alongside the album, featuring both "Peach" and "Every End of the Day".

IU returned to Japan on September 17, 2012, to perform one show, titled IU Friendship Special Concert — Autumn 2012, at the Tokyo International Forum to a crowd of over 5,000 people. With Sunny Hill as a guest act, IU performed a mixture of her own songs and covers of Korean and Japanese songs such as "Juliette" by Shinee, "Friend" by Anzen Chitai and "Aishiteru" from the Natsume's Book of Friends anime series. Live recordings of "Friend" and "Aishiteru" from the event were later released as promotional digital singles. Nearing the end of her Real Fantasy tour and promotions in Japan, IU resumed her hosting duties on Inkigayo after taking a three-month leave due to concert commitments. She also became the host of MBC's short-lived television quiz show, Quiz Show Q, alongside Park Myeong-su and Sun Bom Soo. On December 29, IU hosted the 2012 SBS Gayo Daejeon alongside Bae Suzy and actor Jung Gyu-woon. She was selected by the program's producer for her MC skills that she demonstrated on Inkigayo.

For her accomplishments over the past year, IU won two awards at the 2012 Seoul Music Awards; Last Fantasy was named Record of the Year, while she was among the ten musical acts who were awarded the Main Prize. At the Korean Music Awards, "Good Day" was named Song of the Year and Best Pop Song, while she was named Female Musician of the Year (Netizen Vote). Billboard magazine named IU as one of the hottest musicians under 21 years old in 2012 for her "unique charm and undeniable hits have made her into a bona fide superstar".