Ask them how long they'll continue to offer you fee-free banking and preferential loan rates. As of recently, they offer free banking anyway, as long as you make more than three transactions per quarter online or by 'phone (IIRC).
NIB have offered free banking for ages now, and I find their online banking services much better than BoI's.
What are your criteria for choosing a bank - e.g. charges (preferably low to none - see [broken link removed]), interest payable on deposits (see the ), branch network availability, online banking (what specific features) and so on?
See this previous thread, particularly laragh's post. I use the text alerts to notify me (a) of any unusually large debits and (b) of my balance on a Friday evening, so I can make sure the account never goes overdrawn and attracts charges.
It's not just the online banking features I like, though — the manager and staff in my local branch happen to be particularly helpful and 'on the ball'. I would do without BoI altogether if it weren't also my employer's bank, which helps in terms of clearing payments faster. I also have a BoI [broken link removed] card, but none of those account details are available online — five years after they assured me that this was 'in the pipeline'...
Ulster Bank offer free banking to all of their personal customers.
Their regulare current account has no hidden charges you can make as many transactions as you want, use online banking, set up standing orders etc.
They have 1 account which is a packaged account called the U-First Account and their are loads of benefits like - discounts on hotels, restaurants, flights and 25% off concert tickets this account is €9 per month.