You're staying at the GCH, right? That's the only way you can use the GCH entrance. If so, using the GCH park entrance is usually the way to go, HOWEVER, that can occasionally be problematic. I've done this a few time when someone in front of us was having trouble (tickets won't scan, security issue, whatever) and if that happens, it can really slow things down because there aren't as many CMs/entrance points at that location. But in general, it's the way to go.
The entrance is inside the hotel, near the Napa Rose restaurant, and leads directly into Grizzly Peak. It opens the same time as the main entrance EE at 8:30. I've heard some reports that it opens a few minutes early but I haven't usually been watching the clock that closely. I usually see people recommending arriving 30 minutes before EE begins to be among the first guests through, but I've seen a long line at that time before. We always do at LEAST 45 minutes, often an hour, so that would be at 7:30 tomorrow morning if you want to be among the first in line. The CMs will check your GCH room key and your park ticket.
Keep in mind that RSR doesn't run during EE. Your options would be to go where they hold guests for the CarsLand rope drop and wait there the 30 minutes until regular opening rope drop, or use your EE to ride something nearby, then head to CarsLand. This would mean you won't be among the first in line and may have to wait 30 minutes or so to ride RSR, you just have to decide what's most important to you.
Fastest way to Carsland from the GCH hotel entrance: After you pass through the GCH, you'll be in Grizzly Peak right in front of Grizzly River Run. Take a right. You'll pass Soarin' on your right. Keep going, you'll eventually pass Little Mermaid on your right, then the San Fransokyo/Pacific Wharf bridge will be on your left. Cross over the bridge and you'll be at the CarsLand/Pacific Wharf rope.
One more thing to keep in mind is that it's not uncommon for RSR to be down first thing in the morning. If this happens, you just wasted your entire EE on a ride that's not open.
Have fun!
