You'll have a great time no matter what. See the Castello Sforzesco in Milano. I went there one Ferragosto weekend and the town was E M P T Y and walking around there was so peaceful.
Venice, if you go to Lido, find a nice beach bar/club where you can enjoy chilling for the day, having lunch, aperitive time. I imagine its not much different than a place like Rimini but more expensive. Just get into the rhythm of the day. For Venice, believe me... the further from San Marco, the better the prices and food quality. San Marco should be explored by try to stay in an area like Dorsoduro and just wander backstreets looking for places that serve cichetti. You will get lost but Google maps will help you out.
Rome, explore some of the off-the-beaten path places that are likely to be much less crowded. Sometimes its nice to get into a park and just chill out for a bit. We used to like to go to Villa Celimontana, not far from the Colosseum. Near there you can visit something like this which should be quiet... https://www.coopculture.it/it/poi/case-romane-del-celio . Also, duck into random churches. I used to like going into Basilica dei Santi XII Apostoli since it was a beautiful church and usually empty. Also, check out lesser-visited museums like Palazzo Venezia. June will be a beating in Rome so seek quiet moments. Trust me. I've spent an awful lot of time in Rome and now we spend our time in Italy elsewhere. I've been many times and there's a lot I have not seen so Rome can be visited many many times and each visit can be different. Agree about going to Tazza d'Oro. Get the granita. Also, go to Ostia Antica and/or The Appian Way.
Our summer trip in Italy will be based in Mattinata, Puglia and Rimini in Romagna with little stops on the coast in Le Marche and probably time spent in Bologna to see friends.