Use regional trains. You can play around with bahn.com or the DB Navigator app, where you can select "local transport only”.

Be aware though that the Italian timetable is still far from complete for journeys from 9 June.

Nice - Ventimiglia by TER

Ventimiglia to Milan - as above, select local transport only. But the Intercity is only €3 reservation cost

Thank you guys. Am i correct, that the RV 3379 from Ventimigiglia to Genova is reservation free? 

But im unsure about E3462 from Verona to Brennero. Does anybody know this one? 

They're both RV trains and reservation-free. DB calls them RE.

One more question. If i use the travel planner or the seat reservation tool on the interrail website, are all the shown trains included in the pass? For example Regional RE2636 from Verona to Milano is operated by Gruppo Ferrovie Nord Milano, which isn’t shown at the “Railway companies covered by the Pass” site on the website. 

If a train shows in the results and doesn’t have the words ‘Not in Pass Network’, then you can travel.