Ladies and Men’s jackets

I really like these jackets/pullovers and have a few. Great for layering and good warmth to weight ratio.
https://www.llbean.com/llb/search/?freeText=airlight&init=1

You might take a look at the 32 Degrees brand puffy vest or jackets. They are inexpensive but squish down really well and will fit under a rain jacket.

I am pretty cold tolerant so usually manage with just a 32 Degrees puffy vest layered under my waterproof rain jacket. To me the rain layer is the most important! I want waterproof, an adjustable hood and roomy enough that I can put a warm layer under as well as a small purse.

If you have a Costco membership, they usually sell the 32 Degrees brand there. Sometimes the website has more color choices but is a couple of dollars more than Costco.

Agree about Costco. Other good sources are REI, Sierra and Eddie Bauer. REI and Sierra have excellent return policies. I haven't shopped at EB in a long time, so I can't say. I bought an EB puffer with a hood from Costco last year for probably $20. I made a little stuff sack for it, and that makes a great pillow on the plane. I also use a packable rain jacket over the puffer for rougher weather.

I recommend Uniqlo and always pack one of their puffy vests or long sleeve puffy jackets when travelling. The jacket was perfect when in Italy during March. They are extremely lightweight, pack down into a small pouch and come in a variety of colours. The vest can be layered under jackets as well. There are different styles, some with zips (in the side pockets as well) or button down. Easy to order online

I bought a white rain jacket for about $12 at Costco, about 6 years ago. I probably got more use out of that jacket than almost any other piece of clothing I own. I layer it with a quilted vest that I also bought in Costco.

For those cities, in March, I'd take a puffy jacket..those are usually very light and will not wrinkle.
Bring gloves if you are going early in March.