I'd like to visit Hilton Castle in UK. Which would be best town to stay in?

By any chance do you mean Hylton Castle up in the NE -- it is in Sunderland??

There is no Hilton Castle, it's spelt Hylton. It is in Sunderland, a mainly industrial; area in England's North East. It would be difficult to visit as a day trip from the south, The nearest larger city is Newcastle on Tyne which is about 20 minutes train ride centre to centre.. Here's the website for the castle:

https://hyltoncastle.org.uk

Be aware that it's closed Sunday, Monday and Tuesday and only open from 11am to 2pm on the other days. It's about 10 or 15 minutes by road from the station but it's very small and not really what you'd anticipate as a castle.

The two best zones to stay in Sunderland (very much a rust belt city, not a town) are along the river downtowards the docks and the National Glass museum, a bit high on pubs and restaurants but a nice enough place. Alternatively stay on the northern shore of the North sea, Roker Beach or better Seaburn (basically fish and chip shops and beach stuff but with the odd pleasant hotel mixed in with the trash).

Do study booking.com carefully