It's arguable, but at the time at least, I think you could make the case that Lily was at least somewhat unhappy with the Sorting Hat's decision. Using very much the same source as DVK, we have:
Lily took off the hat, handed it back to Professor McGonagall, then hurried toward the cheering Gryffindors, but as she went she glanced back at Snape, and there was a sad little smile on her face.
Harry Potter and the Deathly Hallows - p.539 - Bloomsbury - Chapter 33, The Prince's Tale
So obviously she's sad that she's unlikely to end up in the same house as her friend Sev and this has obviously taken the sheen off of her Sorting.
But, given that she "hurried toward the cheering Gryffindors", we might think that she was nevertheless excited about her new home. However, so far, all she really knows about Hogwarts has come from Snape and her only interaction with Gryffindor and Gryffindors so far - the conversation on the train between James, Sirius and Severus - has been negative:
James roared with laughter. Lily sat up, rather flushed, and looked from James to Sirius in dislike.
'Come on, Severus, let's find another compartment.'
Harry Potter and the Deathly Hallows - p.539 - Bloomsbury - Chapter 33, The Prince's Tale
A point that's underlined in the very next sentence.
Harry saw Sirius move up the bench to make room for her. She took one look at him, seemed to recognise him from the train, folded her arms and firmly turned her back on him.
Harry Potter and the Deathly Hallows - p.539-40 - Bloomsbury - Chapter 33, The Prince's Tale
So it's hard to imagine that her primary emotion wouldn't be a certain sadness that she wouldn't be with her friend, since she's not really come across much that would make her happy to be in Gryffindor. She might have been ready to give it a chance, sure, but she must have been a bit unhappy and one wonders whether that feeling didn't grow a little as James was Sorted into Gryffindor too.
However, it depends what time-frame you're looking at, because Lily obviously quickly settles in, as Slughorn's recollections demonstrate.
'[...] I used to tell her she ought to have been in my house. Very cheeky answers I used to get back, too.'
Harry Potter and the Half-Blood Prince - p.71 - Bloomsbury - Chapter 4, Horace Slughorn
And the thing is, given that the whole point of the Sorting Hat is that it looks inside your head and finds where you belong, I would imagine everyone would eventually settle in and find themselves at home in their house. Unless, of course, they're the sort of person who wouldn't really be at home anywhere - but then that person isn't going to be thinking wistfully of the greener grass of some other house, so it's not really a case of being unhappy with the Sorting Hat's decision, because they can't really argue with it, there's nowhere they would have preferred to go.
Perhaps the most interesting example of this is Neville. I would argue that in the first book at least, Neville was pretty insecure about being in Gryffindor and feeling like he didn't belong. Maybe for a while he was pretty unhappy about the Sorting Hat's decision and would have preferred to find himself in a house with slightly more attainable ideals.
'There's no need to tell me I'm not brave enough to be in Gryffindor, Malfoy's already done that,' Neville choked.
Harry Potter and the Philosopher's Stone - p.160 - Bloomsbury - Chapter 13, Nicolas Flamel
But he sure grows into himself, doesn't he, and that, surely, is what the Sorting Hat is there to see: just what you can be.
