I'd be torn between a studious life and a creative one.
I love to learn, and spend a lot of time thinking about religions and philosophies and the like. So part of me would love to just vanish away into the cloisters of the college in Winterhold. I'd study the esoteric mysteries of life, safe in the halls and courtyards of the college, venturing out occasionally to go find some scroll or book or artifact, or to visit some significant site.
That would be nice, but it wouldn't be very sociable. I'd only really interact with other mages, except when I went out...
As a real-life archer, I tend to gravitate towards bows in games, too. There's the option to be a hunter, I guess - but I'd rather do something on the creative side. Some have already said they'd go for being blacksmiths, and I do like that idea. But if Skyrim was real life and I could (hypothetically) be anything that such a society could use, I think I'd like to go a little more specific and be a bowyer and fletcher. I could settle somewhere like Riverwood or even Whiterun, and make bows and arrows to sell from my little workshop; maybe even offer training to aspiring archers in the fields at the back. I think I could enjoy that life.