The nearest airport is Bologna Guglielmo Marconi Airport (IATA: BLQ) and is served by Ryanair, WizzAir, EasyJet, Lufthansa, Air France, Aeroflot, Klm, Turkish Aerlines and several other airlines.
From Bologna Airport to Rimini train station there is a direct bus. You can buy and check the timetables directly on the website.
The nearest airport is Bologna, but you could probably consider Milan (with 3 airports), Verona, Ancona, Venice and also Rome depending from your trip.
The highspeed trains network works quite well, Bologna is the closest hub for Rimini.
Best way in general is to reach Bologna with an highspeed train and then take a regular train to Rimini.
For the bus connection you can check this page, flixbus has also a stop in Rimini.
Car sharing is a cheap way to move around Italy.
Rimini is close to the A14 - Autostrada Adriatica, a 743 km motorway that goes through the east side of Italy, from Bologna till Taranto.
Rimini is served by two exits: Rimini Nord and Rimini Sud. With the A14, from Rimini it is easy to reach the A4 to Venice and the A22 to the Brenner pass. Florence, Rome and Naples are equally accessible with the A1 motorway.
If you have additional questions, please check the official web site of Rimini.