Would you be commuting by car or public transport?
You can have a look at our guide to Areas and Suburbs in Dublin for a few ideas. From what I can gather on Google Maps, it looks to me like the following areas are within a travel time of 25 mins or less to Beaumont: Clontarf, Ranelagh, Ballsbridge, Donnybrook, and Smithfield.
As Anonymous mentioned above, there is a shortage of available housing in Dublin, and for what is available, prices are quite high, so it's best to start looking as far in advance as possible.
Best of luck with your move.