Barcelona or French Riveria (Nice)

They are quite different. Barcelona is a city. Outside of Nice (lots of art museums), the Riviera is a bunch of small towns.

I would take a train between Paris and Nice rather than flying, but at 5 hr. 45 min., some folks would make the opposite decision. It's also possible to get to the Cinque Terre (I checked Monterosso) from Nice by train, in about 5 hours.

So I think the Riviera fits better into your itinerary from a logistical standpoint. However, you might reasonably not want back-to-back destinations that are small, coastal towns.

Going to Nice maximizes your time in your plan you can take the train from there to Cinque Terre instead of flying to Barcelona and then having to fly to Italy from there to reach Cinque Terre and Milan

To be honest, your itinerary involves so much hopping around in 2 weeks that I don't think you will enjoy it. I would strongly recommend that you either add another week to your trip (which will allow more time on the ground between your pinpoint destinations), or cut down the number of far-apart places you're going to visit.

What is your intent in going to the Cinque Terre? Do you wish to relax in the small villages? Walk/hike the sections of the trails that are open (a few of the easiest paths are still closed).? I only ask because that will help modulate how much time you'll need. It can be difficult to fit all four destinations in.

Nice to Paris is a tossup with TGV vs. planes -- it really depends if you will be near the airport when you depart. The train will often work out better for more people. I might be tempted to drop BCN and save it for another trip. Or drop Nice and fly direct to Genoa. Or skip the Cinque Terre for post 2021 (depending on your fitness level and desire for hiking).

If you went to Barcelona, you would be visiting three different countries. While all three share the Euro currency, you would have to contend with changes in language and customs.

We took the train between Paris and Nice, and found it very enjoyable. It allows you to travel from the center of one city to the center of the other. For a trip of that distance, you really don't save any time by flying.

Seeing your other post and looking at what you propose, my first reaction was much like epltd, yet another destination is probably not what you need.

If another location is what you want, I think logistically, Barcelona is the less desirable choice.

Flew into Barcelona and spent 5 days there , beautiful city had a great time, then flew into Paris and spent 7 days in Paris . We had been to Paris twice before so we didn’t have to rush around to all the tourist areas . Had a great time in both cities . Would have liked to spend a few more days in Barcelona to travel around a bit more .