Short answer: Yes. There are two monumental mausoleums that are still standing in the city Rome itself, that of the Emperors Augustus and Hadrian.

The Mausoleum of Hadrian – now the Castel Sant'Angelo – was built in 123-39 AD and was an almost an exact replica of the Mausoleum of Augustus which had been built over a century earlier. This mausoleum was said to have been based on the original Mausoleum, that of King Mausolus (whence 'Mausoleum'), built in the fourth century BC and one of the original Seven Wonders of the World.

The Mausoleum of Augustus was the tallest building in Rome for over half a century until the construction of the Colosseum in the 70s AD. You can still visit both buildings (i.e. the Mausoleums of Augustus and Hadrian), though the Mausoleum of Hadrian is in rather better shape than that of Augustus, which has long since been ransacked and is now frequented by lots of stray cats.

The Mausoleum of Augustus was designed to hold the ashes of not only Augustus but also his family/descendants. This is where the ashes of Tiberius were laid after his death in 37 AD. Caligula's ashes were also laid there after his death in 41 AD, as were those of another Emperor, Nerva.

Note: ashes, not bodies. One of the reasons we don't have the bodies of Roman Emperors is because they were typically cremated rather than buried. If anything, we'd be looking for cinerary urns rather than skeletons in coffins.

The Mausoleum of Hadrian contained the ashes of seven Emperors: Hadrian, Antoninus Pius, Marcus Aurelius, Commodus, Septimus Severus, Geta and Caracalla.

Both the Mausoleum of Augustus and Hadrian remained untouched until the sack of Rome by Alaric and the Visigoths in 410 AD, at which point the ashes were disturbed.

The ancient sources tell us where other Emperors ended up, too. Trajan's remains were buried at the base of his famous decorated column, which you can still visit in Rome, while the ashes of some of the Flavian Emperors (those that followed Nero but preceding the Nerva-Antonine dynasty) were placed in the Temple of Vespasian and Titus (located at the western end of the Imperial Forum in Rome, between the Temples of Concordia and Saturn.)

Just going to throw this in too. In Istanbul we have at least four surviving porphyrr marble monumental tombs of Emperors, sadly unmarked and inscribed. We do have a shard of Constantine the Greats in the Istanbul archaeological museum. Furthermore, while the Church of the Holy Apostles was demolished by Mehmet II and with it the burial place of every Emperor fr Constantine to John Tzimiskes (d.976) part of the Pantokrator monastery remains which was the burial chapel of the Komnenoi dynasty (1081-1185).