I was pre-tenure at a regional state U (SLAC) and was moderately unhappy. I was on the market for three years, turning down a bunch of offers over those years largely because I couldn't summon up the courage. In my fifth year on the clock, I got an offer this spring and accepted. I move out this summer.
I had letters of reference from my department chair and from two other faculty members. I explained the rationale to them quite clearly: my wife needed a good job in her field, and also we wanted to live closer to family. I did not mention that I was moderately unhappy at my post, although I think they all recognized this.
One day couple years back the chair called me in to tell me that he was going to write that I wasn't a good fit for the department. He provided no real rationale, but it was clear that my desire to move was a factor. I was pissed, and told him so. After all, I have been great in the teaching and also super in the research. We eventually patched things up, but I knew then how risky it can be to be honest about one's career.
Academia is a strange place. The idea of tenure (at least, traditionally) was to preserve academic freedom and integrity. But somewhere along the way it morphed into this weird social clique- if you show any signs of rejecting them, they may take it out on you. You have to watch out for their feelings and make sure that their ego isn't hurt. My wife is not academic, and she has had no issues in telling her colleagues, who are all uniformly hopeful towards us.
That said, I am glad that I had those letters of support. My sense is that search committees were a bit weirded out since I was in my fifth year. So I am very grateful that I had those letters.
I agree with much of what has already been said. I would be upfront in the cover letter about the rationale. I placed my rationale at the end of the letter, just a couple of sentences. I focused (more positively) on the greatness of the new position, rather than my bad fit at the old institution. Also, don't bad mouth anyone from the current place (not that you would, since you clearly like your position there).
After I announced my decision to leave, most in the faculty were either apathetic or sullen. Actually, all the senior faculty were apathetic and sullen (moreso than usual). But in general, I was surprised at how little was offered to me in my exit. I was their colleague for close to six years, and I am leaving without even a farewell lunch. But it is for the best, for their lack of emotion only confirmed my decision to leave.