Bangor has a jobcentre on the High Street. Start there.
Bangors key employers are Ysbty Gwynedd Hospital, Bangor University, Gwynedd Council and the Retail Sector.
There are also industrial/business estates at Llandegai, Parc Menai (as well as smaller ones such as Tregarth)
It depends on what you're after, theortically there's everything from the lowest paid dull job to a Brain Surgery Position!!
Have a look at Jobs which are advertised at the jobcentre, and if nothing suits seek out the businesses you'd like to work for, speak to people there... you might get on an email list, find out about an upcoming job or at worst get to know the area and a few people as you go.