There is a shuttle stop in front of the hotel. That's your best bet. If you head in just before it opens, there should be parking inside the gate, but it fills up usually within the first hour. All the major tourist spots are not accessible by car, to limit congestion and accidents...hence the shuttle. Hikes are everywhere and at all skill levels. So take the shuttle to a trailhead, hike, get back on the bus to the next trailhead, etc. The most popular hike is "The Narrows", which is pretty much a full day adventure...but this time of year the water will be almost freezing. Can't really dress warm, since you will likely be half or full submerged depending on the depth of the river. If taking the shuttle, be sure to get back on time. If you miss the last one, you will be hoofing it several miles back to your hotel. You and a few hundred others will all have the same goal, so don't try to cut it close. The hotel entrance is NOT a comfortable walking distance, especially if starting your day. There are ample restaurants within easy walking distance of the hotel though.

Breakfast was available early enough to eat and get out to catch the first bus up to the park. It got us there before the booths were open and we were able to simply walk in and catch the park bus to the top of the park and were in the Narrows by 8am

I don't know since we didn't have one with us.

It's 1.5 hr. away.