Should I book Italian trains now or buy tickets locally?

Pisa to La Spezia and the Cinque Terre are regional trains and can be bought when you are there. They are always the same price and have no reservations.

Cinque Terre to Bologna are regional trains as far as Florence, then a Freccia train to Bologna. You can buy that when there as well as Florence to Bologna is a relatively short trip, so likely no big discounts.

Bologna to Vienna should be bought as soon as it is available to secure a discount. You may find the best price from OEBB, the Austrian carrier that operates these trains. It is almost a 10 hour train journey with a train change in Innsbruck.

For regional trains, there is no advantage to booking early. The price doesn't change, there are no reserved seats, and they don't fill up. For faster trains, you can often save money by booking in advance. The Trenitalia app is very convenient. to use. (I didn't see the previous response until after I posted; sorry to repeat).

Thank you! Silly me I meant Venice not Vienna!

Yes, go ahead and buy tickets for Bologna to Venezia S. Lucia as soon as they become available to secure a discount, being aware that you must pick an exact train and the ticket is only valid on that train. If you want to maintain flexibility, you can buy when you are there, paying full price.

Thanks Sam.

The only reason to buy any ticket ahead of time is for the discount that MAY be available. But discount tickets have limitations -- mostly no refund and no change. The Regionale train ticket is the exception as it good for any Regionale train within the time period your Regionale ticket is valid. The price of a Regionale train ticket never changes.

Ok Thanks this is really helpful. Looks like I have a fair few options.