If you would like to explore from Northallerton by train the North East Rover may be of use. This ticket offers 197 miles of travel on the East Coast Mainline from Retford to Berwick on Tweed. The area covered is bounded by Newcastle - Carlisle - Settle - Bradford - Halifax - Huddersfield - Sheffield - Retford - Cleethorpes - the North Sea coast plus Newcastle and Berwick on Tweed. Northallerton falls within this area. From 2013 includes the Harrogate line.
Any 4 days in 8 - £88, child £44.00 and with a railcard £58.10. Not valid on Hull Trains or Grand Central trains and only after 08.45.
Any 7 days £102, child £51.00 and with a railcard £67.35.
Grand Central Railway is a relatively new company operating London to Sunderland trains and these stop at Northallerton in each direction.
They are what is classed an open fare operator and can set their own fares - consequently they are significantly cheaper than East Coast who operate London trains via Northallerton.
An advance single to London can cost as little as £12.
There are only four trains each day in each direction but as such great savings can be made it is worth booking with Grand Central.
Northallerton is on the main London to Edinburgh mainline and East Coast trains stop here. Also served by Transpennine Express trains on the hourly Manchester to Middlesborough route or the equally frequent Liverpool to Newcastle route but not all the trains on the latter route always stop here.
I travelled by train from Leeds to Northallerton when I visited. It cost me 17 gbp (October 2011) for an advance day return but this would be considerably more if I booked on the day. First Transpennine Express offers direct trains from Leeds to Northallerton and takes approximately 1 hour to 1.5 hours. East Coast Trains also offers direct trains to Northallerton from London and Newcastle.
Northallerton is on the Moors bus network although it is only served by one bus to and from the town on the Moors Bus network. However by taking the train to Thirsk there are a greater number of buses on the Moorsbus network from here.
Moors Bus is a summer only scheme operated to enable people without cars explore areas of the North Yorkshire Moors not usually served by bus.
The buses interlink reasonably well and fares are reasonably low. There are a number of buses with disabled access.
The website (which is very detailed and well thought out does need some navigating but this is a welcome innovation for the area.