I need to propose an addendum to Els rule about all Italian sites being closed on Monday. If Monday is a public holiday the sites are open, but the following day (= Tuesday) they are closed. At least that's what I learnt the hard way when I showed up in Cerveteri the Tuesday after Easter Monday. It had been a two hour trip from Roma Terminale to the site and I stood in front of a closed gate. I had checked the website before and it did not have any notice of Tuesday being closed.
Without hesitation I did what any seasoned WHS traveller would do in such a situation. No, I did not climb the fence or bribe the guards. I also didn't throw in the towel and head back to Rome. Instead, I accessed the Unesco page and openend the map of the inscribed property. Coming up to the museum gate I had already noticed plenty of tumuli and caves, so I figured that the core zone may well extend past the museum's fence. And indeed: The core zone of Cerveteri is way larger than the fenced area of the museum. Several tumuli are open all year round. The same applies to plenty of the burial caves. Especially, on the back side of the site you get great views and I would encourage you to go there in any case. In addition, there are several spots where you can peek through the fence.
Getting There
Roman public transport is a mess. I have counted four (!) different public transport providers, each with their own tickets. The Rome 24/48h/.... pass won't help you at all as soon as you leave the rather small confines of the town center. I don't recommend getting any form of pass.
To make matters worse, several of the transport options are not listed on google maps. I found another app which had better coverage of Rome and Lazio: moovit. I can recommend it if you plan to travel in the area. It's not complete nonetheless and it won't help if you bus is stuck in traffic as happened to me.
As far as I understand it there are two options to get to the site:
There is a direct bus from Rome. While probably the most comfortable option, it's also fairly slow as you need to make your way past the Roman traffic. Note: You need a suburb ticket from Cotral to ride the bus. If you buy the ticket on the bus you pay a hefty surcharge.
You can take the train to Ledispolis-Cerveteri and take a bus from the station to Cerveteri. The local operator is neither on google maps or moovit, so ask around. Their tickets can be bought outside of the train station at the news stand. They are not, however, accepted in the Roman bus. Alternatively, you could also take a cab.
From the city center of Cerveteri it's a 2km walk up hill to get to the site.