Hello
We spent 10 days in Taormina at the beginning of June on our honeymoon - our boutique B&B was amazing but being a honeymoon was more at the higher end of prices. see www.casaturchetti.com
Taormina is about 45 mins from Catania airport by taxi transfer cost about �60.
There is a train station at the foot of Taormina but that itself would be a taxi or bus ride.
There are lots of places to stay in Taormina which is a beautiful old town that is easy to access by foot, with a greek amphitheatre, lovely small alcove style beaches, lots of restaruants and trendy bars etc designer shops etc.
It's easy to organise day excursions to Mt Etna, the Aeolian Isands and a local town where the Godfather films were set.
Check out tripadvisor for hotels in taormina and also this was an old article form the Guardian from 2004 & 2006 but it's an interesting read...
http://www.guardian.co.uk/travel/2004/jan/24/i taly.culturaltrips.guardiansaturdaytravelsecti on
http://www.guardian.co.uk/travel/2006/apr/22/i taly.onlocationfilminspiredtravel.guardiansatu rdaytravelsection