I've done this a couple of times (the train) - it's a LONG day, but it's also usually very scenic (well it is in March when I do it). I wouldn't want to mess with driving, even if it would be quicker (and it would save 2-3 hours). I'd imagine around the time the OP is looking at it, the train departs in darkness and arrives in darkness, and it's probably only really light out around the Denali area.

There's a dining car and you can get okay hot food on board - it's not gourmet by any stretch of the imagination, but it's not bad either.

When I've done it in the past, you could combine a one-way train trip with a one-way Alaska Airlines flight for around $220 all-in. This allowed you to take the train up (or down), spend as much time as you wanted in Fairbanks, then pop the quick flight down to ANC to catch connecting flights back to the lower 48 or spend some time in/around ANC.

EXP_Cougar - If you're doing FAI, you need to be popping over to Chena Hot Springs Resort. Great opportunities to view the aurora, plus (as the name implies) a hot spring which is quite toasty. The rooms are nothing to write home about - they can be big, clean, and well-lighted, but otherwise plain. They do nightly snowcat tours to a nearby hilltop where you can see in all directions and there is no light pollution. If the skies are clear and the lights are out, the view is incredible, magical, and any number of other adjectives.

If you're not kitted out, stop at Big Rays in downtown Fairbanks for gear - obviously it will be very cold up there then, especially if you plan to spend time outdoors stargazing.

Have a blast!