Tinos can be easily reached from Rafina (near Athens) where there are daily ferries going to the Cycladic islands. The journey takes about two and a half to five hours depening on the boat you take. On the airport of Athens there are regulair busses going to Rafina, and you don't have to drive through Athens itself. Of course you can also take a taxi. The ride takes about half an hour. It's also possible to fly to the island of Mykonos. From there it's only 30 minutes by ferry.
For schedules and a possibility to book a ticket -