The safety of the lots probably depends a lot on which airport that you go to. Also, I agree with one of the other posters in that make sure you check the cost of the parking lot versus a limo. But anyways, back to your question, I park my SUV at the Manchester, NH airport all the time in long term parking without having any problems. I have parked it there many times for 1-2 weeks.
Now, when I am flying out of Logan in Boston, I always take a limo because:
1) Parking is expensive.
2) Even though it has gotten better, getting to Logan can be a pain.
Have a great trip!