I was waiting for someone to answer this, but after two days of no responses I decided to dig into this myself! This was a bit of difficult task, as most extensive biographies of the Habsburgs tend to be in German. However, there were enough quality sources in English to get a general idea of his post-abdication life.

For some background, Ferdinand I Habsburg was the Austrian Emperor from 1835 to 1848. His parents were related many times over (supposedly double first cousins - Habsburg intermarriage to keep titles within the family was legendary), which is generally considered the reason for Ferdinand’s multiple health conditions. He suffered from severe epilepsy, hydrocephalus (water in the brain), which made his head abnormally large, and a general weak condition both physically and mentally. While being mentally impaired, Ferdinand was still said to have had artistic talents and interest in natural science and technology. He also was a gifted linguist and apparently spoke five languages. Regardless, he was unable to perform the routine tasks of being emperor, and the nation was de facto ruled by a council of family members and politicians, most notably Klemens von Metternich.

During the Revolutions of 1848, the ruling council concluded that having a Ferdinand as emperor was no longer feasible given his many disabilities.The empire was in open revolt and needed a decisive leader to save the monarchy. Ferdinand was persuaded to abdicate in favor of his nephew, Franz Joseph, who proceeded to crush the revolution (with help from Russia).

Now to actually answer your question. Ferdinand retired to Prague Castle, now in the Czech Republic, where he spent most of his time. In the summers he spent time at a chateau he owned in the small town of Reichstadt, (now Zakupy, in the northern Czech Republic). He seemed to have a love for architecture, as he had multiple parts of Prague Castle and his chateau at Reichstadt renovated or reconstructed. As “Duke of Reichstadt,” a title he still had, he had extensive lands around Reichstadt and seems to have put them to productive use. While being mentally impaired, Ferdinand still seemed to have had an aptitude for acquiring wealth. He was shrewd enough to assert his right to his father’s inheritance, and through various means acquired a substantial fortune over the next 30 years. Ferdinand occasionally provided financial support to Franz Joseph as his “wealthy uncle.” Upon his death in 1875, Reichstadt and Ferdinand’s fortune went to Franz Joseph, who was said to have remarked, “All of a sudden, I am a rich man.”

All and all abdication seemed to be a good deal for Ferdinand. No longer under the pressure of being emperor, his health improved, and he was beloved by the local population. Once out of the limelight, he got the opportunity to pursue his hobbies and seemed to have a pleasant life post-abdication.

Sources:

Ferdinand I, Reichstadt - The World of the Habsburgs, Schōnbrunn Group

Landmarks – City of Zakupy website (translated from Czech by Google translate)

History – Prague Castle visitor’s website