Hi,
I have been with HSBC in Fethiye and also in UK and have only had great service from them.
We are insured with Intasure from the UK they cover all contents buildings and earthquake extra cover however you must still have the compulsary DASK insurance locally, this can be purchased in many offices in the town but I beleive you will have to have tax numbers and passports to purchase.
There is a thread on this site with details if intasure and a link to their site.
I hope this helps,
Mark.