Hi forum! My friend and I are planning a trip to Italy for the month of May and any comments/criticisms/suggestions would be most welcome as it's my first time in the country.
We are late 20's/early 30's, well traveled backpacker types. Both very much into hiking so would love to get out to some natural spots...art fans so museums are a must...and, most importantly, obsessed with all good food and drink...so we'll be eating our way through the country.

May 2-5: arrive Florence, explore city, museum, 1 day to explore Chianti wine area by bus
May 6-7: train to Cinque Terre, hiking, overnights in Monterosso
May 8: travel to Siena
May 9: explore Siena, overnight in a TBD airbnb house etc maybe Montepulciano?
May 10- 14: Tuscany goodtimes w/ rental car or motorcycles. Check out hot springs, Maremma, day trips to little towns.
May 14: travel to Naples
May 15 - 16: Naples (1 day city, 1 day Pompeii)
May 17-18: Ischia Island with 1 overnight
May 19-22: Amalfi Coast (hike Path of the Gods?)
May 23: travel to Rome
May 24-26: Rome
May 27: catch flight to Barcelona

Anything I'm missing? Any nature spots/walks/hikes we may want to visit?Spots that we may be lingering for too long in and may want to consider another destination? We have the ability to potentially add an extra day or two to our trip so if there's anything we simply must add to our intin, would love the intel

When you said you had a month, I envisioned what I would do with the luxury of that much time. But you actually only have 24 days not impacted by arriving/departing, and you're talking about staying in 8 different hotels. All the places you mention would be appealing (I've been to all of them), but not all 8 (hotel) destinations would make my final list.

You have three coastline destinations (CT, Ischia, AC). I'd skip one of them, probably the CT.

Maremma is pretty far from the usual first-time Tuscany itinerary. It's at least 2 hours from Montepulciano. A lovely drive, but 4.5 hours in the car is still 4.5 hours.

Unless you are very experienced motorcyclists (in both dry and wet conditions), I would stick to a car.

If you really are art and museum fans, you might want to add more time to Florence and Rome.

Oh, I see now that your title says 3+ weeks...

While I don't really see any glaring problems, you might concentrate it a bit more, as Jean suggested--for more time in fewer areas. There are two hiking books devoted to the Amalfi coast and the islands offshore--you might start there to see if you would like to allot more time there (could allot your CT days there).
The Maremma area may need more research--some trip reports here may be useful.
happy travels!

Any nature spots/walks/hikes we may want to visit?>

I enjoyed very much hiking up to Ravello from Amlfi town - a rather steep at places stepped trail traversing a lush valley with fruit trees and small farm plots to Ravello - a site in itself with stunning views over the whole Amalfi Coast and beyond.

From Ravello I hiked down a zigzagging paved path thru vineyards - with the sea in full view the whole way.

So those short sweet but steep hikes are great IMO!

Ischia but not Capri? Not saying I liked one more than the other but Capri, away from the hectic boat dock and Blue Grotto areas is very neat - I walked across the middle - twas great!

Thanks all! The advice has been incredibly helpful. I think we may end up saving Cinque Terre for another trip, in order to allow ourselves more time in Amalfi and possibly Rome or Florence.

As far as islands - thought Ischia might be a good pick to avoid some of the tourist beaten path, but any more thoughts on Capri vs Ischia?