Rimini has an airport connected to several European cities.
Next closest airports: Bologna (1hr), Ancona (Falconara) (1hr), Venice (2.5 hrs) and Milan (3hrs).
Rome has two airports: Ciampino and Fiumicino (also known as Leonardo da Vinci).
The most popular low-cost company that may be useful to you is Ryanair.
If you are flying to Italy from non-European airports you will likely land either to Milan or Rome.