Day Trips from Vernazza, Rome, Florence

The Cinque Terre is best seen by visiting the adjacent cities taking the hiking paths between them. It's a destination and has enough to see and do without taking in other sights.
Rome is worthy of the full 4 days to its self. You could possibly find a tour company that could take you to a couple of the many travel sights out in the suburbs that most travelers never see--like Palestrina.
Florence travelers will often take a day trip by bus down to Siena. Or you could rent a car in the city and head south and southwest visiting Tuscan hill towns. On our last trip, we visited Certaldo, Orvieto, Volterra and San Gimignano by rental car. Many travelers will also stay in Tuscany on agriturismos, which are farm stays.
You could take a quick train ride over to Verona from Venice. Or, you could rent a car and head north into the Dolomite Mountains.

For your fisherman/outdoors loving husband, just being in the Cinque Terre should feed his soul. Are you walkers? Obviously it is a great place for hikers/walkers. You can take some of the trails or just tour each of the towns for fabulous sea views. Rick Steves has a self-guided tour in each of the 5 villages that will take an hour-or-so each. Then take the boat from Riomaggiore to Monterosso and enjoy the views. If after all of that you need more, take the boat to PortoVenere or a train/bus-or-boat combo to Portofino.

From Rome, Ostia Antica and perhaps a bit further on to Lido di Ostia for lunch by the sea.

Florence: consider a ToursByRoberto non-wine tour for the history and beauty of the Chianti countryside.

Here are some other towns close for a trip from the Cinque Terre
http://blog.ricksteves.com/cameron/2016/05/italian_riviera/

If you are adventurous and have a car you can always go Canyoning in Carrara close by. http://www.tateam.it/canyoning-en?lang=en_us

While I agree that 4 nights is probably the bare minimum for Rome, if you need options for half a day trips from there, the already mentioned ancient Roman port at Ostia Antica is well worth it and just 30 minutes out from the terminal at Roma Ostiense. Lake Bracciano and the Odescalchi Castle are 1h north by train, Tivoli is 40 minutes away, on average, from the Roma Tiburtina train station - once there you can either visit Villa D'Este, Villa Gregoriana or Hadrian's Villa.

In addition to trips to other Tuscan towns from Florence (Siena, Pisa, Lucca, San Gimignano, Arezzo, etc), I see it's only an hour from Florence to Ferrara. I've been there twice on day trips and liked it a lot; look into it to see if it appeals to you.

Take a half day trip to Lucca from Cinque Terre. It has a wall around the old town center which makes for a shady, beautiful bike ride. We loved it there... In early June it smells like flowers... I wish I knew which kind......It's delightful.

Venice for 3 nights is only 2 full days and maybe a few hours the day you arrive. You only have time for Venice and maybe Murano (glass) and Burano (colorful façades).

Florence for 4 nights=3 days+1/2 day on the day of arrival. You could potentially take one or two day trips, depending on how much time you want to devote to Florence.
Siena+San Gimignano, Arezzo+Cortona, Lucca+Pisa are three popular day trips that are easy using public transportation.
The Chianti Hills and also Volterra are better done with a car.
Fiesole, on a hill overlooking Florence, is also a popular side trip with the city bus (no. 7 bus), but it won't take you a whole day. Fiesole would be good for an evening dinner trip cum night view of the City. Fiesole has also Roman ruins and a museum. If you want to see that, you need to go earlier in the afternoon before they close.
Cinque Terre should be done between Florence and Rome, not between Venice and Florence. 3 nights aren't much. But if you want to take a day trip, Porto Venere is good and so is Portofino and the nearby San Fruttuoso Abbey.
4 nights in Rome might give a chance for one day trip. Orvieto is a popular one. Above you received some good suggestions as well.