Echoing the above, if you've only 7 days - and especially if any of those 7 days include travel to/from Italy - then I wouldn't try to do more than 2 locations. With 10 days you could do 3 with maybe 1 day trip. You do need to be in your departure city the night before your flight home (USA?)
WWII sites: you might find this previous thread helpful:
https://community.ricksteves.com/travel-forum/italy/wwii-museum-in-rome
And this blog (not mine but by a respected, frequent poster on TA):
https://blog.spanishstepsapartment.com/2020/06/15/world-war-ii-sights-in-rome/
As mentioned, the classic first-timer's trip tends to be the "Holy Trinity" of Rome, Venice and Florence. Venice would be your 'water' spot; Florence is the cradle of the Italian Renaissance, with more priceless treasures of those periods than you can get your head around; Rome, of course, contains a wealth of ancient history and is a pilgrimage destination for Roman Catholics. Seen one of these cities and you've seen Italy? Far from it! Italy wasn't a unified country until 1861; the three cities listed, along with others, were once regional city-states with their own unique governments, cultures, ruling families, etc; history, architecture, art, regional cuisine and dialects vary between them.
It's not difficult at all to fill 3 days in each, keeping in mind that 3 FULL days = 4 nights. 3 nights = approximately 2.5 days in each. You could consider arriving in Venice for 3 nights; Florence for 3 nights; Rome for 4 nights and flying home from there.
Your active group might enjoy a long hike on the Appia Antica in Rome. More on that if you're interested?
Alternately you could split your trip between Rome and a base in Sorrento or Amalfi Coast. Fly into Rome, go directly to the coast, head back to Rome for the balance of time and fly home from there. You might look at Salerno as a base as it has good rail between Rome (and Pompeii, if interested) and ferry/bus services around the coast. It is also probably less pricey than some other locations in the regions, and has seen some love on the RS forums. While very pretty, getting around the coast can be a challenge as it's very busy and their overloaded transport system can be slow (road) and packed (buses & ferries).
Budget: you will be traveling during high season, all are very popular destinations, and are not particularly inexpensive. Some forum posters are fond of monastery stays: they offer little in amenities but are budget-friendly, safe, clean, quiet and usually include breakfast. You could also consider apartments; good for saving on meals eaten 'in', and more room to move around although they can have their drawbacks regarding check-in times, cleaning fees, no desk staff for help, etc.
Just a start?