I'm living in Berlin, but never stayed there in a hotel ;-). The opera house is quite easy to reach by underground (It has its own underground station) from one of the most central underground lines.
I just took a look where the leonardo is. You should easily reach the opera by foot with 10 min.
cheers 757DUD

PS: you should consider at least one performance in the "staatsoper" Unter den Linden. It is a nice old prussian building