During the Julio-Claudian dynasty the urban horti, large estates owned by wealthy aristocrats on the edge of the city, were nearly all confiscated by the emperors, particularly Claudius and Nero.
Many emperors preferred these 'urban retreats' to the Palatine, notably Vespasian. The emperors also held many extra-urban villas where they resided whenever they wished.
Some examples (early empire only):
Bay of Naples Various
Centumcellae Trajan
Lorium Antoninus Pius , Marcus Aurelius
Alsium Marcus Aurelius
Nemi Caesar , Constantine
Nola Augustus
ad Gallinas' (via Flaminia) Augustus
Lanuvium Augustus , unknown 2nd cent.
Praeneste Augustus
Tibur Augustus , Claudius , Hadrian , unknown 2nd cent.
Capri Augustus , Tiberius
Alba Augustus , Tiberius , Gaius , Nero , Domitian
Antium Augustus , Tiberius , Gaius , Nero , Hadrian
Anxur (Tarracina) unknown 1st cent.
Circeii unknown 1st cent.
Neapolis Marcus Aurelius
Laurentum unknown 2nd cent.
Tusculum unknown 2nd cent.
Puteoli unknown 2nd cent.
Baiae Augustus , Gaius , Claudius , Hadrian , Marcus Aurelius , Severus Alexander
Capua Antoninus Pius , Severus Alexander , Caracalla
Campania Vespasian , Severus Alexander