Is it better to do a round trip flight to a specific location and then branch out from their or fly in and fly out at different locations
Generally the "open jaw" plan allows you to see more without having to backtrack -- especially in a long, narrow country like Italy. Consider, for example, flying into Milan and departing out of Rome or vice versa.
Both times we visited we did open jaw flights. the first into Rome out of Milan, the second time into Florence out of Venice.
Usually better to fly "different locations" - or what we call "open jaw." Buy as ONE ticket not TWO one-way tickets! When searching (e.g. in Google Flights) use "Multi-city" to search so you can check the price as one ticket.
Sometimes it is still cheaper/better to round trip. It all depends what kind of flights you can get, budget, etc. A classic trip would start in Venice end in Rome - that was my first trip to Italy. But, I could get a direct flight to Rome to start and a better flight home from Rome than Venice. Had I flown into Venice, I would have had to connect to another plane, have a layover in Europe, etc. And it would have cost more. I flew into Rome instead, a simple, easy, direct flight, and then immediately took a train north (without staying in Rome) and came back to Rome at the end and did all of my days there at the end. But if I could have gotten a direct flight to Venice instead, I would have done that.
It depends on your plans. Sometimes a loop works just fine, sometimes it's better to not backtrack. What are the destinations?
We are going to fly into Venice and out of Rome. It cost us maybe a $100 more each to do it that way, but will save time and money not having to backtrack.
It is difficult to get a direct flight into Venice. We are going to leave out of Chicago and fly to Toronto for our layover instead of having to do the layover in Europe in the middle of the night. United Airlines/ Air Canada Rouge to Venice and United back from Rome.