There is alot you need to consider, if your ages are of a standard retirement age then you must consider health facilities. Health wise for the future, you would not want to be in a mountain village for instance. Look for somewhere that has regualar all year public transport. You will be entitled to IKA here and need the relevant form , check out the DWP website in the UK. This entitles you to medical care from the IKA clinic. Also consider that most islands, should you need surgery or have a more serious illness , will send you to the mainland for any serious medical care. Sorry to be all doom and gloom but i have met retired people who end up trying to sell their home as they are in the wrong location.
For a bank account they will want to see your pension earnings, you can get a tax number here from the local tax offices, a residency paper from the police. Have a search on line for estate agents on different islands and they often have rentals so this will give you an idea of the cost on each island. If you will have lots of family visiting you should look at the cost of flights to the island, for example Corfu has Easyjet now during the summer which if booked in advance is cheap.
It is best to do internet searches on the islands you are interested in and take it from there.