In All Things Under the Sun: How Modern Ideas Are Really Ancient, author Lindsay Powell lists ancient writers who contribute to our knowledge of Roman personal life through their writing, especially correspondences:
Supplementing these famous writers, whose work was copied over and over by scribes and made it through the Medieval period to our time, are the soldiers' tablets from Vindolanda and the hodge-podge of correspondences from Oxyrrhynchus.
A public domain book on the topic, is The Private Life of the Romans, by Harold Whetstone Johnston, Revised by Mary Johnston; (1903, 1932). See its
bibliography.


Comments
Also Juvenal and Martial. The latter gives a very real feel for the sheer inconvenience of life in ancient Rome.
Pliny’s letters in the Penguin translation are wonderful. Cicero’s letters to his friends are also good, but hard to obtain in a modern translation (the Penguin is out of print). The letters of Cicero to Atticus are a bit stodgy for me.
Suetonius is certainly readable.
The good thing about all these authors is that you can read a few pages here and there.
I’m surprised Nepos, Athenaeus, Seneca and Diodorus haven’t been mentioned; they all provide insightful anecdotes.
I would definitely add Seneca and his Moral Epistles to Lucilius. Even though these are not true “letters,” rather a moral education written in the form of letters (much like Plato’s dialogues), they do supply thought-provoking comments on such things as gladitorial events, the treatment of slaves, the morning regime of salutatio, extravagant foods and bathing.
Martial’s “Epigrammata” (see my FB page: Martial’s Epigrammata) provides a wonderful look at upper-class life, as does Pliny’s letters. But there’s so little material on the lower classes. It’s a shame.