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When it comes to safety, the choice of route is usually very low on the list of concern. Even in the dead of winter, the oft-repeated advice of "go south" can actually be a fools errand, especially if a southern route would had hundreds of miles to the drive.

But in your case, by the time you get to April, the chance of winter weather in all but the highest elevation spots is fairly low. More importantly, you've got 5 or 6 days, which is a very nice amount of time to make this trip comfortably on almost any route.

Since you're traveling with 2 cars, I'd try to stick to the interstates, just because I think that will make things a lot easier - you won't have to worry about getting split up with traffic lights or other cars or missing turns. So for example, if you decided to take I-40 across Arizona, I would not follow the US-54 route across Kansas that google often suggests.

Beyond that, I would take the route that looks most interesting to you.