Train: the location is about 10 minutes walk from the station (main entrance on the West side, platform 1), maybe slightly more on return (uphill!). From Leeds, trains are at least half-hourly until around 20:30, hourly after that. The last train back is 23:18. From York, trains are half-hourly at about 11 and 41 mins past the hour until 20:11, then hourly, last direct train back is 22:05. In each case, journey time is about 35 min. (Correct at time of writing - please check times before travelling.)
Bus: The location is also about 10 minutes from the bus station where there are services to and from the local areas; in addition, there is the frequent 36 Leeds and Ripon bus (drops to hourly after 9-ish in the evening).
Car: Parking in Harrogate can sometimes take a bit of searching. You may find a space on the nearby streets such as Valley Drive or Montpellier Gardens, or if you're really lucky, directly behind the pub. For those who simply can't get enough smartphone apps, there is "AppyParking" which shows any free on-street spaces.
Foot: From the Railway Station, head a short way N to the pedestrianised Cambridge St (Cafe Nero on corner). From the Bus Station, head S to the same. Walk along Cambridge St and, at the end, pass the War Memorial and turn right down Parliament Street past Betty's.
Location: The listing coordinates are for the Wintergardens, now a Wetherspoons pub. Food available. Sorry, no dogs.