we travelled around Chios by scooter/moto, which, despite a couple of incidents, was a great way to see the island. We hired them from somewhere in Karfas (don't remember the name) but there are loads of places to hire motos from. we payed about 10 euros per scooter a day.
Just a couple of warnings... if you are inexperienced at riding a scooter - be careful! my friend ended up in hosptial for 3 days after crashing his scooter!! secondly, we decided to cross to the other side of the island through the hills... and didn't realise quite how much petrol we'd use... so we ran out, and it seems that petrol stations are few and far between!! fortunately one of us had enough fuel left and went off to get some for the rest of us, but it was a slightly frustrating situation!!
Despite those couple of incidents, I'd highly reccomend scooters as the best way to see Chios!
From Norway, Denmark, Germany, Switzerland, Belgium and the Netherlands there are charter flights to Chios. You can also easily take a flight to Athens and catch a plane to Chios from there. There are several daily flights.
We hired the taxi for the whole day and it was very reasonable. The gentlemen took a liking to us and showed us some off beat places.