Update: As of Saturday, November 3, 2007, the roads to the Griffith Observatory were re-opened to private vehicle traffic. The observatory shuttle is no longer running, and there is no longer any cost associated with visiting the Griffith Observatory. Read more here and here.I had some time today, so I made a 12 noon reservation for the Griffith Observatory this morning. I also wanted to see what it would be like to hike from the Greek Theatre parking lot.
There is a roadblock set up at the Greek parking lot. The city workers will not let you drive up past that point, but they wave through the observatory shuttles and employees in private vehicles and vendors.
I parked my car at the parking lot. The ticket (it's free, but you need to enter your credit card information to hold the reservation) says you will need to show the ticket to park at the Greek Theatre, but there was no one checking tickets when I arrived around 11:20. There is also some street parking across from the lot.
The road up to the observatory is fairly steep, but shaded by trees. You have to be careful because the edge of the road falls away downhill in places. I walk at a fairly brisk pace, and enjoy hiking, and it took me 15 minutes to get up to the observatory. If you are in decent shape, I can't imagine it would take more than half an hour.
I noticed that there were two or three dozen cars parked on the road leading down from the observatory parking lot, and probably another two or three dozen cars parked in the lot. I asked a Park and Recreation worker, and he said the cars all belong to employees.
I found it a little strange that employees aren't required to park in a remote lot and take a shuttle to the observatory. When the public demand dies down and the observatory shuttle stops running, a good percentage of the parking spaces will be taken up by employees, and parking at the observatory will be considerably more difficult than before the renovation, when the employee area was a small part of the parking lot.

I arrived at the observatory about twenty minutes before opening, and there was a small crowd milling around in front. I spent the time walking around the building and taking pictures, and when I returned just before noon, the line waiting to get in stretched across the front of the building. We were forced to enter through the new underground entrance. A large number of the visitors were eager to see the new planetarium show, and while the exhibit areas were not so crowded, a long line formed in front outside the building to buy tickets for the planetarium show. I believe the planetarium show runs every hour, starting at 1 pm, but I didn't have the time to see it today.
I noticed that the hiking path that goes down from the east side of the observatory down the ridge to the lower side of the Greek Theatre was cordoned off, both at the top of the path, and a few hundred feet down, near where the observatory was fenced off during the renovation.In my opinion, the hiking path is not the best option. It does allow you to walk without vehicle traffic, but 1) it's very steep just up from the Greek Theatre area 2) there is almost no shade, and you would be fully exposed to the sun or wind 3) there is a point at which the path crosses a vehicle service road, and it's easy to lose the path.