least wear n tear drive from Colorado Springs to Salt Lake City in August?

With Interstate 70 closed through Glenwood Canyon due to mudslides, there's really only one option: take Interstate 25 north to Interstate 80, then take I-80 west to Salt Lake City.

Google offers the option of cutting the I-25/I-80 corner via US-287. That saves about 20 miles, but US-287 is typically one lane each way with narrow shoulders, while the interstates are two lanes each way with wide shoulders. If your car does develop a problem, the interstates offer a better option for pulling off to the side (and a tow truck is likely to get to you faster).

If you drive, you'll buy about $200 in fuel, the trip will take two to four days of your time, and there will be some wear on the car.

I'll go one further than @NateEldredge: consider flying direct from Colorado Springs to SLC and return. Delta flies several non-stops each day on this route. Flying will cost about $100 more out-of-pocket than driving, but it will save two to four days of your time, remove car-related risks, and there will be no wear on the car.

If you can do your business in SLC without a car (or can rent or borrow one for a day or two), this may make better sense than driving the whole way.