I'm familiar with your area--we come out that way fairly frequently, as Marilyn grew up in Aberdeen. But it sure is lowlands, compared to this part of the world.
I've spent most of my flying life in the high country, after first learning to fly in Anchorage in late 72 and 73. I instructed in Laramie for several years in the 70s and 80s, in 160hp 172s, and I did SE charter all over Wyoming and northern Colorado, mostly in 182s. So I have some suggestions.
Lean properly! If you haven't yet flown your airplane very high, do so, so that you can get the feel for how much less power you have at altitude, even leaning properly. When taking off from a high elevation airport, lean on the ground during the run-up. There are those who say that you must do it at full power--I disagree. Use normal run-up rpm, pull the mixture out until the rpm just begins to drop, then back in about half an inch or so. If you have more sophisticated instruments than the average 170, then use them to adjust mixture to best power. I find that I don't do any better with my Insight engine analyzer than just the method I just described.
With 170hp, you shouldn't have too much trouble maintaining a decent altitude. Since your experience in the rocks is limited, I suggest that you just climb up to 11,500' and stay there for much of your trip. You have 2 major mountain ranges to cross, the Cascades east of you and the Wasatches east of the Salt Lake valley, and it's best if you have your altitude well before getting there--don't ever try to climb up to the crossing altitude as the elevation rises below you. One specific place, if you fly as far south as Salt Lake--don't try to climb up Parleys Canyon east of Salt Lake (that's where I-80 runs)--again, get your altitude before hand. For one thing, locals often come down through Parleys westbound, and there's not lots of room to miss them.
You didn't indicate where you plan to stop. I wouldn't recommend some of the places others have suggested, only because of your limited experience in the mountains. I like Granby, and I love Marble, but they're on the west side of the rocks you really should avoid, and they are no place for inexperience. Similarly, some of the favorite spots in Idaho aren't for inexperience. As far as cities go, Pocatello and Idaho Falls and Twin Falls are nice. Small towns: hard to beat Afton, WY, home of Aviat which builds Huskys. I wouldn't recommend any of the other towns in southern Wyoming until Laramie, mostly because of distance to town from the airport, unless you decide to stop at Saratoga.
Following I-80 across southern Wyoming is best, to MBW, then south to Laramie and on south to KBJC. I would not recommend cutting the corner toward Saratoga, unless you plan to lay over there--it is a nice tourist stop, and it's easy walking distance into town from the airport. If you do go to Saratoga, leave by following the extended centerline of runway 5, which points at a saddle between Elk Mountain and the Snowy Range (aka Medicine Bow Mountains on the sectional). Unless you're familiar with the territory, it's easy to get confused if you try going southeast, and you can easily find yourself on the west side of the mountains. If you go through the saddle, then on toward Laramie, that's the easiest.
When actually crossing mountain ranges, early in the day is best. But otherwise, I've flown all over the west at all different times of the day (and except in the mountains per se, at night, too), and it's not an issue. It's usually windy, but not overly difficult, other than when you head back home, you'll undoubtedly fight a headwind.
If you have specific questions, please ask. Lots of very experienced pilots on this board who are anxious to help.
Cary
