I'm planning a trip to Italy...any opinions on how to best spend a week there? (no rush)

And never eat at a place that has pictures of the food on the menu.

absolutely, I’d also suggest just walking 5 minutes up the backstreets away from the main tourist places and see what’s there. The cafe’s and restaurants we found by doing that were unfailingly good and reasonably priced even they were never in the style of “fine dining” (whatever that is). We found Trastevere particularly good for that.
Just by taking on board a couple of simple tips that have been mentioned already we found it hard to eat badly in Rome.

I’ll second Telemark’s and SanVito’s advice about not trying to cram too much in widely separate places. And RickG’s advice about Cinque Terre is spot on. I might suggest starting there for a couple of days, then moving on by train to Florence for a few more, then to the wedding. Last I heard, CT was putting a cap on tourists (good!), so you’ll want to look into that and make sure you book early. All of the five towns are gorgeous.

If you’re looking for more scenery/hiking than arts/culture, I’ll also recommend the Dolomites, like TwoCarrotSnowman. We were there in June in 2019 and it’s breathtakingly gorgeous and the weather in June is great.

If you do go to Rome, make a reservation at the restaurant Spirito Divino in Trastevere. It’s the best meal I’ve ever had in my entire life. (Or meals, I should say, since I went back on our next trip and it was just as good). Incredible, tiny, family-run restaurant. The host/owner is very charismatic, likes to chat with guests, and their wine cellar is housed in the remains of an ancient synagogue I recommend the pork shoulder.

We spent two weeks, visiting Rome, Sienna and Florence. The museums alone could occupy all your time. The Uffizi in Florence and the Borghese in Rome are must-sees. Have an espresso and something light for breakfast, then spend your day going from gelato stand to gelato stand, then have a good dinner at a non-tourist restaurant; don’t order pizza. I really wish we could have visited the Italian alps, but just didn’t have time. You can’t swing a dead cat in Rome without hitting some historic and awe-inspiring architecture or statuary. I’m a huge fan of Bernini and his “David” statue is in the Borghese, as is his “Rape of Proserpina”. Michelangelo’s David is at the Academy Gallery in Florence.

I’d just second all the advice not to rush. Personally I would just camp for the week somewhere. You could stay a week in Florence and still feel that you had not spent nearly enough time there.

My rule is that 3 weeks is an absolute minimum time away, and five weeks is where it gets to be too long living out of a suitcase. One week is just enough to get a taste for things but not enough to make the overhead of the trip worthwhile.

Thirded. I spent a week in Florence a couple of years back, and that was just about right for one city. Then a couple days in Venice and home. Worked out perfect, but I can’t wait to go back, perhaps Bologna then train to Sienna or someplace. Italy deserves a measured approach, not approached flashmob style.

My dad and I did a tour of Italy back in 2012 and in Rome I loved the Colosseum and the Castel Sant’Angelo.

Florence I didn’t care for - I’m not an art museum person - but enjoyed La Specola Museum. This was on my father’s bucket list due to its collection of wax anatomical models.

We also went to Venice, but you’ve been there. Then to Lake Comp to see dad’s oldest brother at the columbarium. I like Bellagio and the old church that was there. And taking a ferry from the village where my uncle and his wife lived in the summers to Bell ago and back.