I second Vigna di Valle, fantastic, and a beautiful location.
There is also a terrific museum about 40 miles southeast of Rome, can't think of the name right now, they have many large buildings full of stuff, half of it local history and half WW2. It's the place that has the P-40 that was pulled off the sea floor off of Anzio. Only a few airplanes there but lots of other neat stuff including four Sherman tanks.
Incidentally Anzio is a nice little town, worth a trip. Not much in the way of battlefield sites, a small museum, but if you go be sure to visit the British and US cemeteries. If you do, read Bill Mauldin's account of Lt. General Lucian Truscott's speech at the dedication of the US cemetery, extraordinary. In fact everyone should read about it anyway, it makes my eyes water every time:
https://www.cnn.com/2015/05/23/opinions ... index.htmlOf all the places we've been I think Italy was our favorite vacation.
Edit: found the name of that museum, Piana Delle Orme
http://pianadelleorme.com/pages/-