Check with the hotel. You may get tons of posts from people, myself included, that have parked (either a park n ride rate or just paying for parking) at an airport and taken a shuttle BUT you don't want to wind up with a hotel that doesn't have enough parking and limits it to the time you're actually staying in the hotel.
Sometimes a hotel that's actually on airport property doesn't have any parking, if you need to park you'll wind up parking in the airport lot.