I tend toward the mild-medium or medium end of the spectrum in the morning, though I'll smoke almost anything if i have a specific craving.
But I particularly like lanceros in the morning. Lanceros are more relaxing to me for some reason, and a nice calm morning is a great time to sit down for a long smoke (if I have the time). My favorites lately are:
Tatuaje Especiales
My Father Lancero
El Triunfador #6
El Triunfador Lancero Especial (maduro)
Otherwise, I'll go ISOM in the morning many times. Lately I've been into HdM which I think make great morning smokes, and Bolivar is nice in the morning, the creaminess in both those lines goes well with coffee. Yesterday I had an H. Upmann Mag 46 which was just ridiculously good.