I had refugee protection in Italy under the Geneva convention with a Refugee Travel Document. Except for Schengen countries, what other countries can I travel to with this document and don't need a visa.
Depends a little on whether they're Schengen, who it was issued by (in this case Italy), and what the countries you want to travel to think about your country.
The Refugee Travel Document is like a faux passport, allowing you to exit and return to the country that issued it. You're not a citizen (usually) so can't get a passport. Makes sense.
Now of course you'll enter another country with this document instead of a passport, so they have to decide whether to recognise it. Not all will, especially some Middle East and SE Asian countries. Instead of listing them all out, as they may change, I'll refer you to this:
Convention Relating to the Status of Refugees - has a map of the (currently) 145 states which are parties to the 1951 Convention Relating to the Status of Refugees and are obliged to issue travel documents to refugees lawfully resident in their territory, as well as ones who only signed the 1967 Protocol.
Even if they do recognise and will issue documents, you may still need to meet the regular requirements for a visa (eg tourist visa for Cuba, or invitation for Russia), that nationals of your country do, or indeed, potentially additional requirements that the destination country may impose on you, given your refugee status.
As a result, t's always best to check with your state department equivalent before you travel, to ensure your eligibility, as international politics and policies do change.