I think it's meant to vary by encounter, sometimes I'll do 4-5 encounters before needing to rest, using only a couple spell slots/LR abilities each time, sometimes I get absolutely savaged and need to rest after only one or two. /shurg It does get easier as you level, and long rest casters in particular get more resources. Worth noting too, the time-sensitivity of the quest becomes... much less so, shortly. :P Still urgent, but not "you have one week, then you die, and the Absolute probably takes over the world" urgent.
I suspect the game is balanced around the idea you'll probably do 2-4 encounters per long rest though, purely given the ratio of short to long rests.
The Royal Tyrell is a great stop, I remember going there when I was about that age to visit my great grandmother. The Alberta badlands in general are neat, worth stoping by some hoodoos or other similar formations if you get the chance.
As far as other stuff goes:
The Fraser River and Hell's Gate in particular is worth a stop, when you get to BC. (Also a good menory from that trip.)
And while (as an Ontarian) I fully understand the desire to drive though the province as fast as possible, there are lots of great scenic spots in the western half of the province, along Huron and Superior. (As you get into the Sudbury>Thunder Bay stretch, in particular.) There are also some beautiful spots more in my neck of the woods (Thunder Bay>Manitoba border stretch) but by and large those are further from the highway and more of a trek to visit. :P