Bangor has fantastic rail links due to it's position in relation to anglesy and the ferries at holyhead. You can get to london in just 3 and a half hours, there is a train to Manchester every 2 hours. Look at the arriva trains wales website to book your tickets in advance for some realy good discounts, (single tickets to or from Manchester are £10 booked in advance)
Bangor Bus Station is just off high street on Garth Road, by Denenhams, and from here you can get busses to most places in North Wales.
a 'Red Rover' ticket, which allows you unlimited travel within a certain area (it is quite large and will get you to such places as Conwy, Caernaerfon and Llanberis) for one day is £4.95.
The number below is for Travel line, where enquiries can be made about times and prices from Bangor Bus Station.
Bangor Train Station is located on the main rail line to Holyhead, and as such gives the city excellent rail links to Liverpool, Manchester, Birmingham, Holyhead, London and more.
There are some direct trains to Liverpool and Manchester, but normally a change at Chester is required. There are many direct trains to London Euston and Birmingham however.
A return to Manchester is around £30, and a return to London is in the region of £70.
The number below is for Travel line, where enquiries can be made about times and prices from Bangor Train Station. The website is also for National Rail Enquiries.