Rimini is kilometers from Bologna , a taxi would be extremely expensive. Rent a car or take the train. There is a really good bus service from Bologna forli airport which is only 10 euros each way. You can get info on Bologna Forli airport website.
If you are flying from New York you will probably land at Bologna airport and not Forli so the best bet is bus or taxi to Bologna station and than a train to Rimini. Rimini is a big sprawling resort which apart from it's old town,. I fyou are not looking for somewhere over touristy, try Cattolica which is just a bit further down the coast.
I was in Rimini in May, I don't think there is anything dangerous there. Oh no!!!! Try the local buses which have an average of 5 pickpockets a day on them!!! There are many drugs and drug dealers and also the beach is a no go area after dark. Should I continue??
The old part of Rimini is a very nice and interesting place and the area of Marina centro is also nice and has some very nice hotels too. Areas such as Marebello or Miramare leave a lot to be desired. It's one thing having a quick flying visit from Paris and being lucky but take it from me, and I've lived and worked in the area for many years, you need to be careful where you go.
Don't take large sums of cash or passports around with you and be very careful on the buses as they get crowded and thats when they strike. I am not saying you will not find pickpockets like everywhere in the world, but I would not describe Rimini as a dangerous place Rimini is not Rio. I walked along the beach late at night, I've been to restaurants and bars the street behind viale amerigo vespucci without any kind of problem.
