Whether other fans like it or not, the best way to re-build a franchise is to tank for a few years. Being mediocre or a fringe playoff team is pretty much a slow cruel death to those fans.
It's worked for some teams: Chicago (Kane, Toews), Pittsburgh (Crosby, Malkin, Fleury, Staal)
And some just botch it up like Edm (Hall, RNH, Yaks), NYI (under Milbury)
The slow death teams are like CBJ, Wild who had one 1st overall pick and had success too early, and then ended up with lower and mid 1st round picks.
Unless you're like the Wings, where you can mine superstars out of the later rounds, or if you're like jarmo kekalainen who can scout gems, then pretty much the best bet is to tank.