My "favorite weapon" really depends on what sort of character I am playing.
If I am playing as a straight fighter type (Nord, Orc, or Redguard usually), then my favorite weapon is usually Wuuthrad (the two-handed axe you can get after becoming Harbinger of the Companions.)
If I am playing as a mage type (Altmer or Breton usually), then my favorite weapon becomes mid-range Destruction spells (Firebolt, Iceball, Lighting Bolt.)
However, if I am playing as a thief or assassin (Bosmer, Khajiit, or Argonian usually), then my favorite weapon becomes the Nightingale Bow, interspersed with Nightingale Subterfuge (a power that equals Rage spell that tends to work regardless of the target's level.)
BTW, my current character is an Argonian "efficiency expert" who uses the Nightingale Bow (IMO, an "efficiency expert" is one who tries to finish encounters in as few attacks as possible, saving his or her arrows. He or she relies on stealth and Nightingale Subterfuge to even the playing field before making his or her presence even known.)