Hi all, we're heading to Italy in the Fall, and I was just wondering if it's okay to bring a small power cord to plug in our laptops/phones/camera chargers etc, then just plug the power cord into the adaptor that we're bringing with us. That way we'd only need one adaptor. Thanks for any input

Should work fine, Evergreen. I always bring an extension cord (about 6 feet) with multiple plugs for this purpose. Many older hotels have few outlets, often hidden behind furniture, and most are already in use. The wiring for a typical 120v U.S. cord is more than adequate to handle the 240v European current. An adaptor with multiple USB sockets can be useful, as well, if you have a bunch of equipment needing charging.

I, too, routinely travel with a small power strip.

Just make sure it's simple cord and not one with a surge suppressor built in.

Ditto that. A regular cord but NOT a surge protector.

Dumb passive power cord - yes, power strip with power surge suppressor not specifically rated for 240v - no.
>>> That way we'd only need one adapter.
If your intent is to save space, multiple plug adapters would be less bulky than a power cord.
If your intent is to deal with accommodations providing only one usable plug, then your idea works. You can also bring a multiple outlet plug without the bulk of the cable.
One caution about the Italian outlets. They come in two different diameter pin sizes. Newer (most) hotels and hotels catering to international travelers from other European countries provide outlets that can take both 4.8mm (most countries outside Italy) and 4.0mm (Italian plugs found in old properties especially in the South) diameter pins. Many people carry 4.0 mm diameter adopters (Europlug) or have stayed only in Italian properties wtih 4.8mm outlet capability, so it looks like all the plugs in Europe seem to be the same. However, when I tried to use a 4.0mm diameter pin plugs in Vienna, my charger kept falling off the outlet because the pin was too loose. The "Europlug" is a thinner pin type usable throughout continental Europe including Italy.

Thanks everyone for the great advice! I found a travel power bar today that also has two spots for charging our phones...and it says on the back "not a surge protector", so I think I'm set

If you mean it has USB ports many of those things use USB1 and are very slow for large phones/tablets. Your phone may only charged when turned off. Test it at home . At worst you'll need to bring your current phone charger and ignore the ports