Upvote:1
With an ordinary Italian residence Permit (together with a passport), regardless of your nationality, you can visit (at least) Schengen countries, Albania, Bosnia, Bulgaria, Croatia, Cyprus, the Dominican Republic, Georgia, Kosovo, Montenegro, Romania and Serbia.
It does not let you visit the UK or Ireland.
Upvote:1
With effect from Jan 2021, to travel to Edinburgh (the UK), a non-EEA family member of an EU, EEA or Swiss citizen needs a valid national passport, and one of the following:
You cannot use an Article 10 or Article 20 residence card issued by an EEA member state.
Source: https://www.gov.uk/guidance/visiting-the-uk-as-an-eu-eea-or-swiss-citizen
Upvote:4
Your Italian residence permit allows you to travel within the Schengen area and to the Schengen-candidate EU members (Bulgaria, Croatia, Cyprus, and Romania). It does not allow you to travel to the United Kingdom (where Edinburgh is), nor to Ireland.
Ireland is a member of the European Union, as was the UK when this question was asked. For travel to Ireland, the residence permit exempts you from the requirement to have a visa only if the following are true:
This visa exemption is no longer valid for the UK. If you are the family member of an EU/EEA/Swiss citizen who is a participant in the EU Settlement Scheme, see Traveller's answer for the relevant details concerning travel to the UK.