Judging by your kit lens, you have an APS-C sensor (crop factor 1.5 for Nikon or 1.6 for Canon). Full frame sensor lenses would, of course, be different. (18-55mm (29-88mm FF equivalent) is consistent with a Canon kit lens, don't know about Nikon.)
If hiking is the priority and weight is an issue, I generally carry a P&S. However, if photography is a priority I will carry my APS-C sensor DSLR. Depending on the nature of the trip and the expected scenes/subjects, I carry some subset of a wide zoom, a standard zoom, and/or a telephoto zoom.
Some better quality consumer-grade Canon lenses for APS-C bodies for the above categories:
* wide zoom: 10-22mm (16-35mm FF equiv)
* standard zoom: 15-85mm (24-136mm FF equiv)
* telephoto zoom: 70-300mm (112-480mm FF equiv)
(If you check review websites you can get informed opinions on individual lenses.)
If I carry only one lens, it is usually the wide or standard zoom. (I use the telephoto zoom mostly for shooting wildlife from a distance.)
APS-C tends to be medium quality at medium cost and weight. Full frame and professional grade lenses would produce higher-quality images at the cost of a significant increase in the cost, size and weight. One could also use prime (fixed FL) lenses for even higher image quality or larger apertures.
Another option would a wide range zoom, however such lenses tend to have lower image quality. In dusty environments, one might prefer not to change lenses. (Professional grade gear tends to have water and dust sealing which may make them a better choice in such environments.)
Back in my film days, I often carried only a 28mm prime on a 35mm SLR.
The kit lenses are often a good place to start and many never use anything else. The best choice for you depends on your photographic style and expected scenes/subjects.
Doug