As a Classical Archaeology major it is a daunting and anxiety inducing task to see everything and at times this is followed by a reconciliation process with the fact that you may visit a city like Rome and not be able to see everything you wanted. Also, as a Classical Archaeology major it is hard not to feel like you are dragging your sisters around in +35 temperatures to sites they probably don't care about besides getting the AC that they so desperately want. But lets face it, Archaeology major or not, the rich history of the Mediterranean makes it a near crime to not visit at least one museum otherwise you really have not for one, experienced a balanced trip and two seen a little bit of everything you possibly can (basically in my opinion you've missed the point!). What the best thing about places like Rome is that you can pick your time period and go accordingly. Here are my favourite museums in Rome (that are sometimes heavily favouring the classics department):
1. Vatican Museum: I start out with a word of caution: If crowds and waiting in an hour plus lineup is not your thing then you may want to skip and also, if you are someone that likes to spend their time and space with works then the funnelling format that is followed is also not for you. Other than that the Vatican Museum is extensive and chances are what you want to see will be here (ie. Laocoon/Augutus Primaporta)--But be ready!
2. Capitoline Museum: This museum has the coolest layout as it incorporates the foundation of the Temple of Jupiter Optimus Maximus and features some other important works such as the Dying Gaul, Praxiteles' Venus, the Equestrian statue of Marcus Aurelius, and the very important bronze she-wolf with Romulus and Remus.
3. Villa Borghese: The important thing to know is that you need an appointment in order to enter the Villa Borghese and that it is closed on Sunday so do check before heading out. But this museum and its neighbourhood is straight from the Roman Holiday---no really it is. It also houses my favourite statue by Bernini of Apollo and Daphne and features paintings by Caravaggio, Rubens and Raphael.
4. National Etruscan Museum: The forgotten and often mystified period of history in Italy are the Etruscans. Their contributions to Rome and its empire and so Western culture is so important that its sad that they are relatively unknown. It houses the Apollo of Veii and the very famous Etruscan sarcophagi of reclining couples. Sadly, it is quite out of the way, so I understand if its only your love of the Etruscan culture that would take you all the way to its doorstep!
5. Ara Pacis Museum: The Ara Pacis houses perhaps one of the most important monuments of history: the Ara Pacis or in english, the Altar of Peace. A part of Augustus' peace propaganda it is in great condition and represents many important historical and art historical bench marks. If you're lucky you could try to coincide your visit with the light show that projects the Ara Pacis as it was thought to be in its colour form.
The key to museums is to go to the ones that house the things you want to view, then just take your time. Devote at least a day to the larger ones and go during the hottest times of the day but if you want to beat the crowds then go early in the morning! And you have to come to the realization that you may not see everything you wanted. A few points:
1. Make sure to check which dates the museums are open
2. In August a lot of the galleries are not open
I hope this helped!