It is not our normal practice to rise early on vacation, but on the Monday we took the tour we (luckily) did. We selected the tickets that included the audio tour ($20 per person) and headed for the boarding area. There was a line but the wait was less than 10 minutes, and note that you must go through a security check similar (if not more strict) to that in the airport. We boarded our boat and headed for the statue of Liberty and found a seat inside on the lower level. Keep in mind if you want photos find a spot to stand outside. There are amazing views of both attractions as well as those of NYC.
We arrived at the statue, picked up our audio tour, and headed to the line for the monument. This was quite a process. First you are not able to bring backpacks, which I had, and was required to store in a locker. You then wait in another security line and go through scanners, again. It was not a fun process, but it was worth it. The audio tour guided you though the exhibit as you listed to a variety of experts talk about them. Each exhibit had a corresponding number that you programmed into your audio player. This enabled you to listen to as much or little detail as you choose. At the end of the tour you are able (if you are up to it) to walk the 125 steps to the viewing tower. This was quite a hike and, again, worth it for the photo opps and the views. There are a number of tickets available for a tour that goes up to the crown. If you are interested in this, reserve early.
Our second stop was Ellis Island. Again, we picked up our self-guided audio tour and enjoyed the exhibits. This tour was even more enjoyable and, at points, emotional since you heard first hand accounts of people who had experienced Ellis Island.
We enjoyed the entire tour, except the waiting and security, and would recommend it. Again, try to go as early as you can. As we were concluding our tour we noticed full lines and packed boats that included classes of elementary students.