The search for R2-D2 was a mission undertaken by the Protocol droid C-3PO to rescue his friend R2-D2 from a mysterious stranger.
Shortly after the Battle of Endor, Landonis Balthazar Calrissian, wanting to rebuild his colony on Cloud City, saw an ad about recycling old droids for extra credits, decided to go for it. Unbeknownst to him, the ad was actually a trick by General Maximilian Veers and his Imperial remnant seeking to create an army of battle droids to restore the Galactic Empire. Needing a ship to travel to a spaceport on Coruscant, Calrissian decided to borrow Gial Ackbar's ship, the Daisy Mae. He was spotted by R2-D2, as he and C-3PO were telling stories during their time with the Galactic Republic and the Clone Wars. R2 followed Calrissian to the ship, but was soon spotted by him. Figuring R2 could help him, Calrissian decided to take him along. C-3PO, worried about his friend went off to rescue him with Ackbar's help. Taking Ackbar's old ship, the pair set off to find R2.
Once Lando and R2 arrived on Coruscant, they abandoned Daisy Mae and went to a spaceport where they took a transport to Mos Eisley.
The search for R2-D2 serves as the main plot of the 2015 non-canon miniseries LEGO Star Wars: Droid Tales.