Unless something like a war, outbreak of pestilence or a strong spate of international terrorism occurs, fares will go up as the travel date approaches, not down.

Fares for peak season will continue to go up from "now" 'til flight time, not come down.

Fewer and fewer seats at relatively lower fares will be available as time passes.

Fares to/from low-demand cities or cities with substantial competitive schedules are likely to be lower than fares to/from popular cities with very limited service or limited competition. For example, in Italy, as a rule, fares to Milan will be lower than fares to Rome, and fares to Rome are likely to be lower than fares to Florence. On the US side, Chicago and New York are likely, but not always, to have lower fares than Cincinatti and Denver.

A connecting itinerary may save money compared to a non-stop. Example: flying from the US to Switzerland with a connection in Amsterdam may be less expensive than the non-stop to Zürich.

An understandable desire to not backtrack, for example to Rome from Florence, may cost you (serious) money, likely more than the train fare. How much is your time worth to you?