Itinerary help: Which country should we visit departing from Venice?

I'd go to Slovenia, to Ljubljana. Very close, but not the same. You can stay 3 nights in Ljub, then go to Pula or Rovinj or a close part of Croatia. 7 days is not long, and you probably should stay south.

Slovenia is a good option--it was my first thought. But check return flights from Ljubljana, because there's not a lot of service there (understatement).

I flew back to the US from Zagreb in 2015 with just one connection in Europe. I don't know whether that would be possible to California, but I'd guess it would if your airport is SFO or LAX. Zagreb itself is a nice city, but it's about 2-1/2 hours (from memory) from Ljubljana by bus or train. With Zagreb as your departure point, you could spend some time in either Slovenia or Croatia, or a bit of both.

I haven't researched the late-March/early-April weather in either of those places. I know I ran into wet, cooling weather in the first half of October, so...

At that time of year, I'd prefer to be farther south (southern Italy, Sicily, southern Spain), but I'm cold-natured and really intolerant of chilly, wet weather.

Seven days in Italy doesn't go very far because it's a place that's filled with food, art, sculpture, history and culture. It's just such an important travel place.

Have you considered starting (or ending) in Venice and then taking in Florence (with Tuscany as a side trip) and Rome? They are all worthy of more than a couple of days each.

Italy seems to be most international travelers' favorite travel country. I've been going there since 1970, and I never tire of it. We very much enjoy renting a car and seeing Italy off the beaten path--and staying in agriturismos (Farm stays).

You could consider basing the last half of your trip on the affordability of flights back to your home airport. Hit Skyscanner and check fares back home from any city / country that interests you (book direct with the airline though). You have endless possibilities here. I am jealous.

Italy is also a great suggestion. In the Venetio (the area near Venice), there are many large and small cities of historical and artistic significance. Ravenna (mosaics from 500 AD), Padua (Scrovengi Chapel), Bologna, on and on and on. Also there are the Dolomites, which would likely still be snowy.

Agreed, why spend a day getting somewhere else when you're in one of the most beautiful places in the world?? Not sure where you're spending the week with your son, but you could make your way to Milan and fly home from there, visiting Lucca & Voltera in addition to those mentioned above. BTW, Friday March 29th is Good Friday, so the week leading up to it and the week following Easter (March 31st) is a peak travel period and school holidays across Europe.

Go to Google Flights and put in Venice to "Europe," then one way, nonstop, and if you want, a maximum price. Say, $175.

Now you know all the options for a particular day (and they will be different on each day of the week).

You are investing 3 hours for pre and post flight combined, so does it matter if the flight is 2 hours or 3? Go where you will enjoy the most and don't sweat an hour in the air ..... I suspect all of Europe is within 3 hours.

Slovenia was also my first thought - ditto what the others have said!

I am flying in and out of Venice in May,but not because I am interested in Venice. It is the easiest and cheapest way to get to Slovenia .
I am spending a few days in Trieste because I have never been there. From Venice airport a short bus ride to train station https://www.veneziaairport.it/en/transport/venezia-mestre-station.html
Then about 2 hours to Trieste.

From Trieste to Ljubljana about 2 hours by train.
Return from Ljubljana to Venice airport, I plan to book Go Opti airportshuttle,reliable and not expensive.

Croatia would be better if it was later because the convenient ferries would be running (confirm with Venezialines). It may be a tad cool in Slovenia still. I like best the suggestion to explore more of Italy, which is like 20 different countries in one. How about stopover in Ravenna and then head to Marche, perhaps Urbino, then fly out of Ancona?
I hate to fly within a vacation, but heading west to Spain or Portugal might be nice--at least your flight home would be simple and shorter.

Slovenia and Croatia might be great. I think the ferries from Croatia to Italy (Ancona?) will run. Then you could head back up to Venice or wherever you're flying out from.