York is one of the better served racecourses, apart from being a ten minute walk there are special buses and taxis running from the train station too. I don’t attend flat race meetings anymore but going to York was always a pleasure, you’ll have a great time in a great city.
More like a 20 minute (pleasant) walk, if you don’t want to arrive in a dripping sweat, and if the forecast is correct it looks like being a hot and sultry start to the meeting.
Dedicated shuttle buses operate from approx midday opposite the railway station and are around £3 single. Taxis which tend to take a circuitous ‘rat run’ route due to the heavy traffic are around £5 single.
There is also the FirstYork bus service No11 to Bishopthorpe from the station at xx20 and xx50 minutes past each hour which is £1.60 single. Ask for ‘South Bank’ and you can get off at either the Racecourse, or just round the block at the Knavesmire pub if you fancy a pre-race snifter, though that is likely to be chocker from very early doors.
Make sure to get whatever cash you need prior to arriving at the course. The on-course cash machines carry a hefty surcharge, and unless you have a ticket I’d recommend paying cash at the turnstiles as the Card/Cheque turnstiles tend to have lengthy queues.