If you are travelling to Edinburgh for the rugby clinic, below are a few options.
By Car
From the south, depending on which side of the country you are coming from, the A1 on the east coast will take you directly into Edinburgh city centre. From the west coast, the M74 changing to the M8 will bring you into the city bypass where the A71 (Calder Road) will take you into the city centre.
By Train
Any train to Edinburgh Haymarket or Edinburgh Waverly (main station) will take you to Edinburgh's city centre for easy access to hotels.
By Plane
The best Airport to use is Edinburgh Airport itself. From Edinburgh Airport frequent busses will take you to the city centre where the majority of the hotels are. The bus costs £6.00 return and can be purchased from the driver. Alternatively, a taxi from the Airport to the city centre will cost approximately £20 to £25 depending on the time of day and location of your hotel.
If required, Glasgow Airport is also available and would require about 1.5 hour journey to Edinburgh after your flight.
I would not recommend flying into Glasgow Prestwick Airport. It is about 1.5 hours from Glasgow!
