Robert, First of all welcome to Nikonians. I think you will find, as we did, that this place is one of the most useful sites to learn about your camera and how to better use the camera.
Now for the Nikon 18-200. I have the earlier version of that lens the VR model. It was the first lens I bought after the 18-55 and 55-200 kit lenses. I have used it for years on three different cameras and it has proven to do just fine.
Take the comments you hear about that lens with a grain of salt. They are correct. It is a so so lens, compared to the top of the line lenses. However, as a do it all lens it is a great value. Last spring my wife and I went to Hawaii for two weeks. Now, I have way more lenses than I need. But, I took only that lens and the f/1.8 35mm for night work. It did great and provided me with some excellent photos.
I mentioned taking a lot of the comments against the lens with a grain of salt. The reason I say that is that most of the photographers who frequent Nikonians are not exactly your weekend casual photographer. They have years of experience shooting a lot of lenses. They naturally strive for the best results and the best equipment.
If I can use an analogy, look at audiophiles. Some of these guys and gals would turn their noses up at a CD. Give them pure audio from vinyl. I will take their word that vinyl provides purer music. (ten years of flying military jets took away much of my hearing) However, could the average person tell the difference between a CD and a vinyl record? I doubt it. The same applies to the 18-200mm lens.
You and your friends will love the pictures you get from the D7100 and the 18-200. It is a lot easier to have one lens on the camera than to swap lenses. Why do you see so many pros carrying two cameras? One has a wide angle/normal lens and the other a telephoto.
Are the other lenses better? In some ways yes. They may provide sharper outside corners and be lighter. Still, for a all in one walk around lens that can do almost everything, I think the 18-200 is an excellent value.
Some day you may decide you want better. Until then, enjoy whatever lens you decide to purchase. Anyone of them will make you old point and shoot look like a toy.