My cell phone carrier only allows domestic calls; it does not offer any plans for Europe.
Can I buy an inexpensive unlocked cell phone here with a SIM card in the US to use in Europe for a few weeks to call home and locally there. Please advise where, if possible.
This Rick Steves 'Travel Tips' information might be useful -
https://www.ricksteves.com/travel-tips/phones-tech
One option, visit a phone store when you arrive. Ask them to install a new sim card in your current phone. Have them set up your phone to meet your needs. You'll need to save your original sim card so that you can swap it back to your phone when you return home.
I rarely use this, but some people use their free hotel internet wi-fi to make phone calls (Voice over Internet Protocol (VoIP)). There are a number of these apps for your phone to choose from.
https://www.voipreview.org/blog/best-android-apps-free-voip-calls
olga,
It would help to know which carrier you use at home, and what type of phone you're using? Which country will you be starting in?
You can easily buy an unlocked mobile phone that will work in Europe from Amazon, EBay or other sources. When you arrive in Europe, buy a SIM card for use there. You could also buy a phone from one of the travel phone companies such as this one - https://cellularabroad.com/ . Finally, you could buy a phone with SIM card from a phone shop in the first country you visit.
If your phone allows eSIMs (versus the physical tiny SIM card), you can buy and load that onto your phone. I have a Pixel 6 Pro and was able to purchase an Orange eSIM that works in pretty much all of countries in Europe. The advantage is that you can buy it here in the US and get it instantly and won't have to wait. Plus, you won't have the expense of a whole new phone.