York makes for a long day from London, but you can always nap on the 2 hour train ride. Leave London from King's Cross Station (and get there early for a photo op at Platform 9 3/4s if you're a Harry Potter fan!)
There's a lot to do in York, so it's best to plan your day before you leave. Walk around the walls, visit York Minster, the largest Gothic cathedral north of the Alps, visit the Railroad Museum, stroll through the Shambles, take an open top bus tour. If you have children in tow, they might enjoy the Jorvik Viking Center, but most adults claim to be underwhelmed. If you're a fan of the Vikings, however, it might be worth a visit!
Check the National Rail site for tickets, and look carefully for a cheap day return ticket. Prices can vary a lot depending on the time of your train, so decide if an extra hour in York is worth the difference in price.