7 nights in Italy - Venice and Cinque Terre or Venice and Amalfi Coast? or ??

Venice isn't exactly next door to the CT or the Amalfi coast... with 7 nights you'd give up one day just to reach one of those destinations. I would recommend Venice and maybe Lake Como or Lake Garda or maybe even Florence - or - Rome and the Amalfi Coast

Have you been to Italy before? If not, you can get a really good taste of Italy by doing 2 nights Venice, 2 nights Florence, and 3 nights Rome. All are connected easily by fast, frequent trains. Falls in line with Rick's recommendations, too: https://www.ricksteves.com/europe/italy/itinerary Personally Rome is my favorite city in Italy; the history is just on every corner. I liked it more than Venice. Venice is cool, but 2 nights was enough for me.

These are relatively easy:
Venice plus Dolomites
Venice plus Italian Lakes
Venice plus Bologna
Venice plus CT
Venice plus Florence, Tuscany
I didn’t travel south of Rome until my 7th trip to Italy.

If Venice is where you really want to go, then that’s where you should go. According to Google, the drive time to Cinque Terre is about half the time as it would be to the Amalfi Coast.

Rome is easily paired with The Amalfi Coast (Naples is the closest city though). I found Rome to be a very inviting, friendly city and so fun and relaxing. But, if Venice is where you want to go, that’s what you should do.

I just came back from Italy (not my first visit) and flew in and out of Venice. I took the train immediately to Turin, then took the train south to the Italian Riviera for four nights, including two in Levanto (Cinque Terre), then trained back toward Venice, stopping in a few towns before spending the last two nights in Venice.

Flying out of Genoa, Pisa, or even Milan might be more practical for some; for me it wasn't, but it's something to consider. Some airports work better for some people than others. But you might save some time by using an airport closer to the Cineque Terre if you can.

Anyway, 7 nights actually in Italy (not including travel time to get to/from Italy) is adequate for Venice + Cinque Terre (putting aside whether this or Amalfi is a good choice for you - up to you). I love both Venice and the Cinque Terre and had already been to both before. But I might ask if you plan to hike? If not, I would probably not rush to the Cinque Terre; the hikes have always been the highlight of my visits; the towns are nice too but crowded with tourists during the day. You can find hiking trails that are less crowded during the day than others, but the towns are what they are. And they'll be mobbed with tourists in September.

I would do either Rome to Amalfi or Venice to Cinque Terre. You will eat up too much time trying to get to Amalfi and then back for your flight home.

I agree with others who suggest you stay within a smaller radius of your primary destination (e.g. Venice in the north or Amalfi towards the south), but one of your questions has not been addressed. The most accessible town on the Amalfi coast is probably Amalfi (and it's nearby towns). Amalfi is easy to reach by bus or ferry from Salerno. Travel by public transit to Amalfi would be about 2 hours longer than to Monterosso, a popular choice in Cinque Terre.

OK, here is my suggestion.
Fly into Venice, stay 3 nights. First night you will be jet-lagged, remember. You can explore Venice, see the tourist sites, do side trips to Murano and Burano. Wander around the side streets away from the crowds and just enjoy.
Train to Rome, just under 4 hours. Stay 4 nights. So much to see and do, and fly home from there. Have been there 3 times and still haven't seen all I want to.
Remember you use up a lot of time traveling between destinations, so you want to limit that as much as you can.