Help!: new to the area

looking for a route to get to washinton dc (capitol hill)  from Alexandria VA.  any ideas?

also, I'm used to riding my mountain bike, but now that my commute wil be about 12 miles each way and very hilly, should I change to a road bike??? how much abuse can the "skinny tires" take??? any input would be great. I've been biking to work only about 2.5 miles each way for a few years, so still a bit of a novice...