Fargo station is located downtown, but I would not fear leaving my car there for 2 weeks and I beleive parking is free. I am not sure how readily available parking is in summer, in winter when I was there half the lot was piles of snow so what was plowed was near full. Increased summer ridership may make them frown on it. Google shows a station number of (701) 232-2197.
Airport is ~$15-20 taxi ride and has parking for $33 a week if you want to look there. Some of the area hotels may also offer park and fly packages that may work out.