The first Alnwick Station opened in 1850. This was the timetable in 1854. Today’s equivalent would be an X20 bus at 8.38 from the Infirmary, changing to LNER at 9:01 at Alnmouth. That should arrive in Newcastle at 9:27
The return journey today would involve the 5:34 Cross-country to Alnmouth, then the X20 bus would arrive at the Infirmary at 6:39. Slightly later, at 5:57 the Northern Rail to Alnmouth and X18 would arrive at 7:13. Or at 6:44 the LNER to Alnmouth then X18 gets us back at to the Infirmary at 8:13. In 1854 the express at 5:05 was quicker, but the later option took longer.
We haven’t managed to find what the return fare from Alnwick to Newcastle would be in 1854, but in 1858 Mr Geggie would sell you a ticket for an excursion to Newcastle for 2s 6d first class, or 1s 6d in a covered carriage. Based on the Bank of England Inflation Calculator that would make the 1858 costs of an excursion to Newcastle from Alnwick equivalent in today’s money to around £30 first class, or £20 in a covered carriage.