I used to park with QuickPark and Park-n-Fly. The former is a bit better kept, both have decent shuttle service, but both are outdoors.
If your flight leaves on a Saturday or Sunday morning. and your trip is 8 days or less, you can usually get an outstanding valet parking rate at the Westin of about $150---includes one night's lodging plus valet parking in the WorldGateway deck for 8 days. That means you can go from your bed to your airplane without ever going outside, and from your airplane back to your car parked and warmed up for you right outside the Westin entrance---about 10 feet of "outside time".
In the winter, that's a splurge that I'm more than happy to take.