Many of these sights in the city center you can enjoy in a day’s walk. Very leisurely. If it seems like a lot, look at the distances in the map legend. From the Porta Nigra to the Kaiserthermen is only about a kilometer. Some of these things you will see as you walk through the town. Others, like a trip to Olewig or to Kasel take a car or bus. But they, too, are within a couple of kilometers of what is a very busy city. Going to Saarberg, outside of Trier, is a very pretty drive but is really a day trip, as you should really take a time seeing the town and taking in a restaurant or one or more of the many wineries.
This is probably too much to absorb in one sitting. Take some time and google some of the places I suggest. If you have a few days in Trier, you can see a lot.
I went to Trier last year and was in the town for only a couple of hours between trains. I just wanted to see some of my old haunts and to remind myself of some things I knew well when I lived there. I took a walk down from the train station past most of the sights marked on the map (that are in the middle of the city). I was back to catch my train on time.
You don’t want to do things that fast. I recommend just walking through the neighborhoods, taking your time. Seeing stuff is cool. Remembering your feelings and the companionship of your wife in the midst of those things is better.
View Trier in a larger map