the royal york hotel is lovely, if you can afford it i would def stay there. alternatvley york has hotels like travel lodge that are cheap and cheerful and quite new. and the novotel is another cheap hotel, that has a nice restaurant and pool, which is always handy when you have children.
most places centrally in york are within walking distance of the train station, it is actually quite a small city, taxis are very cheap too, a taxi from the train station to the novotel is about £5!
my dh is from york and i lived there for 4 years before moving back down south, all dh's fmaily still live in york and we visit regularly, i think that if your 3 y.o likes trains he will love the railway museum, he is probably a bit young for the jorvik centre yet, but castle museum is good as well.
plenty of nice shops for you, try and get a cream tea in bettys tea shop too, lovely cakes and they have a shop so you can buy far too many naughty goodies! our favourite resaturant always used to be a lovely littel italiann the shambles (another tourist attratction, a really narrow littel alleyway of houses/shops that lean together)called reastaute bari, very friendly towards children and you cans ee into the kitchen. york also has the usual suspects for estaurants, pizza express etc, def not short of good qulaity laces to eat.
talking about this almost makes me wnat to go back, much nicer than reading for nights out, shame its so close to my in laws!LOL!