I am currently level 22, and the best bow I have so far is an elven bow with 40 base damage (non enchanted). I would really like a high damage unique bow, if anyone know where I can get one please tell me. I know this is probably classed as cheating, but I would definitely have more fun with a cool looking, super damaging bow : )

I think all the uniques require quests but you can get an Ebony bow (probably would be about 52 damage for you) in Lost Valkygg near Labyrinthian. The base damage for elven is 13 and ebony 17, the actual damage depends on your skill, perks and enchantments.

Or, why not get a bound bow? Looks different and does serious damage. 24 base with the conjuration perk and a 24 damage arrows too.

In the place where the quest Silenced Tongues (I think), the tomb is called Volenruud there should be a Draugr Deathlord in one of the rooms who uses an Ebony Bow complete with Ebony arrows. I'm not sure if that would be the case with your level....

You could always power level your smithing can craft your own bow...