Train destination from London for summers hols?

[eversomuch]

We're looking for a great, family-friendly destination to reach by train from London in early August for 1-2 weeks. Somewhere our 3- and 5-yr-olds will have lots to do. Originally had a sandy beach in mind, but we're late booking and I can't find any place along the south coast to stay (Bournemouth, Weymouth, Falmouth or similar, reachable by train, are all booked).

So I'd be grateful if anyone had other destination ideas. Doesn't have to be beach. Ideally in a nice sized town with good restaurant options (vegetarian-friendly). Some places I'm thinking are Arundel (would we have enough to do?) and Littlehampton (found accommodation there but is it nice? Sandy?). Or a farm that we could reach by public transport (am I dreaming?).

Thank you!

It might take a few hours to get there but what about Tenby? Lovely sandy beaches and there are a few places nearby like Folly Farm that you can get to quite easily.

York?

If you do want a beach, the east coast (Scarborough/Filey/Bridlington/Whitby?) is probably easily accessible from York by train.

Train up to Newcastle, then metro to Whitley Bay?

How about Alnmouth in Northumberland? The beach is long and very sandy and public transport is very good.

Or if you don't want to go as far a field then Sheringham in Norfolk. Not as nice a beach, but certainly a reasonable place for a seaside holiday.

Also there are lots of places along the north wales coast that you can do by train. Maybe Llandudno?