Search for R2-D2
The rescue mission for R2-D2 was undertaken by C-3PO, the Protocol droid, to save his astromech companion from a mysterious captor.
Prelude
Not long after the Battle of Endor, Landonis Balthazar Calrissian, with intentions of re-establishing his colony on Cloud City, noticed an advertisement promoting the recycling of old droids in exchange for credits, and decided to pursue the opportunity. However, unbeknownst to him, this advertisement was a ruse orchestrated by General Maximilian Veers and his Imperial remnant, who sought to amass an army of battle droids with the goal of restoring the Galactic Empire. Needing transportation to a spaceport located on Coruscant, Calrissian opted to borrow Gial Ackbar's vessel, the Daisy Mae. R2-D2 observed this as he and C-3PO were sharing stories of their experiences during their time with the Galactic Republic and the Clone Wars. R2 followed Calrissian to the ship, but was soon detected by him. Realizing R2 could be of assistance, Calrissian decided to bring him along. C-3PO, concerned for his friend's safety, embarked on a rescue mission with Ackbar's assistance. Utilizing Ackbar's old ship, the pair departed to locate R2.
The search
Upon arriving on Coruscant, Lando and R2 abandoned Daisy Mae and proceeded to a spaceport, where they boarded transport to Mos Eisley.
Behind the scenes
The central narrative of the 2015 non-canonical miniseries LEGO Star Wars: Droid Tales revolves around the search for R2-D2.