You've received lots of good tips in this thread. With such a very short time frame, it will be important to maximize time at the sights and minimize time travelling between them. That's another value of hiring a local guide.
The five gun emplacements that were mentioned in a previous reply are at Longues sur Mer, and not far from Bayeux. Your guide can probably fit those into the touring route.
I've also toured with Dale and he's an exceptional guide. As you'll have a car, you might also contact Chris Emery - http://www.visitdday.com/home.html . Like Dale, Chris is also ex-British military.
As mentioned earlier, The Longest Day is a reasonably good representation of the events that took place that day, although not completely accurate. One interesting bit of trivia is that one of the stars in the movie actually took part in the D-Day landings. Richard Todd, who played Major John Howard in the movie, actually fought at Pegasus Bridge.
There's also an excellent museum in Bayeux and of course the famous Tapestry which describes a much earlier battle, if you have time. Another site that you can ask your guide about is the Maisy Battery - https://www.maisybattery.com/ .
Prior to your trip, you may be interested in reading D-Day by Antony Beevor. That will give you a good idea about the significance of all the sights you'll be seeing. The book describes the experiences of Major Thomas Dallas, one of the 29th’s battalion commanders and his headquarters staff and that was especially cringe worthy, but to their credit they made the landing despite the circumstances.
As you'll probably want to prioritize the American sites, you may not have time for Pegasus Bridge or any of the Canadian or British sites.