We had ADR for Chef Mickey's - drove to CR. At the gate, told the security guard that we had ressies. He asked for ID or WDW room key (didn't cross check with any lists), then directed us to the hotel parking lot. My understanding is that there is a 3hr time limit for parking at the resort for those who have ADRs.
If you are planning to drive to the Grand Floridian, be aware that this resort has the smallest and least accessible self-parking lot on property. You may end up paying that valet charge just to keep from having to cruise around the parking lot for a long time waiting for a space to open up (if you can even get into the parking lot).
At monorail resorts or resorts that are within walking distance from theme parks (like the Epcot resorts), you may be asked at the gate if you have a restaurant reservation, and you may be limited as to the amount of time you will be permitted to park there. If it's not a busy time, you may not.
Some times they will check and give you a 3 hour pass. Sometimes they will wave you right on in.
But you will be able to park at any of the resort hotels where you are dining.