All of the really good hikes are on Humphrey's or Kendrick Peaks. But if you don't want steep, I'd go to the Dry Lake Hills area off of Shultz Tank Rd (I think). I snowshoed there a few years ago, and I don't remember any hills that were too steep. It's definitely in the pines though.
For a bit of a different experience, Wupatki National Monument, is awesome! There are some amazing stone pueblo-type dwellings there. Really cool. It is located NE of Flag and is at a lower elevation, so it'll be a bit warmer. This area is not in the pines. Still worth a trip though. Also, Walnut Canyon, a few miles east of Flag off I-40 is worth a look.
I'm not sure what you mean by "steep", but it's hard to avoid some sort of elevation gain/loss in Flagstaff. In any case, have fun!
"I'm not a vegetarian because I love animals; I'm a vegetarian because I hate plants." A. Whitney Brown