We have a day off on Sunday. Chances are you'll want to sleep / recover / rock silently in a corner, but for those with the energy to get out, here's some suggestions of things to do around Leeds (check websites for Sunday opening times). For train times and prices, see TheTrainLine.
Leeds has some nice attractions worth seeing. If you're walking, then the City Museum and Art Gallery are pretty good for free provincial cultural institutions (much of the Art Gallery is currently closed, but the Henry Moore next door might be open). Also good, if you like that kind of thing, is the Royal Armouries and general Leeds shopping, the most interesting of the latter being in the various covered Arcades. Also worth an explore is the area around the Dark Arches (under the station) and Kirkgate Market. One of the nicest things about Leeds is that it wasn't extensively bombed during World War II, so it has some great architecture -- as you're wandering around, keep looking up! If you have transport, or can afford a taxi, the Thackray Medical Museum is great, and further out there's Temple Newsam. If you're after a night out, there are obviously lots of clubs, pubs and resturants, but there's also four theatres, two cinemas, and a host of other things going on; details on the Leeds List.
While Leeds is all about the dreams of Victorian Industrialists, York is all about the Medieval. It's about 20 mins on the train from Leeds, and a good day out. Worth a visit are the Yorkshire Museum and Minster. Also good fun is Yorvik Viking Centre. There's some nice shops in the Shambles, and train enthusiasts will love the National Railway Museum.
Probably Leed's main rival in the North, Manchester is the city's brash, exciting, cousin. Well set up for entertainment, Manchester has plenty to see and do, and is only about 50 minutes on the train from Leeds. Great for a night out (and there are late night trains back), it is perhaps best known for its LGBT centre Canal Street, which shot to fame in the ground-breaking 90s drama Queer As Folk, and which is definitely worth the pilgrimage if you're LGBT, along with the (sadly now demolished) Haçienda, which led the way in British music for 20 years. For programmers, it has has a special place as one of the centres of early computing and the home of Alan Turing after the war.
If you want to get out of town and into the Yorkshire Dales, you can get the train to Ilkley or Skipton. Ilkley is a small town in Wharfedale, from which you can walk up onto the famous (in Britain!) Moor. There's some lovely walks, both short and long. Back in town, there are plenty of places to eat, though the most notable (if somewhat pricey compared with others) is Betty's.
Skipton is a classic Dales market down in Airedale. Worth a visit is the well preserved Castle, but it's a nice town to just wander around.
Alternatively, you could head by train to Hebden Bridge in Calderdale, which is a great community of thinkers and artists. Most notable for its shops and cafés, there's also an interesting the Alternative Technology Centre on the canal. While it's a fair walk to Dales-like countryside, there's nice walks to Heptonstall (where American poet Sylvia Plath is buried) and Hardcastle Crags.
Also in the area is Haworth, home of the Brontës, though it is a little hard to get to (watch the return buses on a Sunday) -- if you're a fan of the Brontës, the village and Parsonage are definitely worth a visit, and there's plenty of interesting shops and places to eat there as well.