Suggestions on what to do In Cinque Terre and Verona.

I really liked the Giardino Giusti in Verona.

2 nights each, means one full day each, plus a few hours of the day of arrival. Not much really.
At the Cinque Terre, you could walk some of the paths, then hang out in a town or two.
In Verona, it will take you most of the day to see the city's sights. If you have a chance to spend a night at the arena to see opera, do it.

Unfortunately the opera only goes through the end of August...no performances in September.

In Verona make sure you get to the Basilica of San Zeno Maggiore. It's stunning.

2 nights each, means one full day each, plus a few hours of the day of
arrival.

Right. That will give you just enough time to explore all 5 primary villages in Parco Cinque Terre. You can reach them via train or mix it up a little with boat and trail. I wouldn't bother with vineyard tours as the vines grow all over the steep hillsides so you'll see them from pretty much wherever you are. If you're up to it, some of the trails go right through some of them. But with just 2 nights, taking in Riomaggiore, Manarola, Corniglia (do that one early in the morning or later in the day) Vernazza and Monterosso will likely be enough.

Be sure to climb up to some of the cemeteries and churches in the upper reaches of the villages; good way to escape the crush of day-trippers who don't venture far beyond the centers.

laura, in the CT for two days I would definately take a half a day to hop on the ferry and go down to Portovenere. You get to see the villages from the sea and the cool church/castle at Portovenere is a plus. You can buy one ticket for the whole day and ride down the coast, back up to Monterosso and then back to Riomag!. We also took the shuttle in Manarola up to Volastra and then hiked down to Corniglia, kind of a short cut on a hike that takes a couple of hours, nice hike, lots of steps down when you arrive at Corniglia. Lo Posada is a nice spot for lunch/beer/wine on the deck after the hike and before the steps down to the train!

While in Verona this past May, we did a wine tour with Pagus Tours which has tours through the Valpolicelo region. They have many different ones, and several that go from 2-6 pm. That allows time for wandering around Verona in the morning, seeing the Valpolicello region and usually 2 wineries, then be back for dinner.
We arranged it before we left, but their information is available at many hotels and several people we were with (8 max in the group) arranged it that day. We did the 2 Amarones tour and were delighted to see the wine of a tiny winery we had visited on the menu at dinner.

RS's "Italy 2016" book (or is it his "Venice 2016" book? not sure, took both) has a great walking tour of Verona that takes you from the center of town around the Arena out to the beautiful bridge crossing the river, with great descriptions, walking you past many of the historic and artistic high points of the city. Earlier this summer, sis-in-law and I did the walk in about four quick hours, though it could easily be six, if you take it easy and eat and drink your way through.