If the amount they would pay is contingent on the school, my advice is you go through each school’s NPC with them and see if they will commit to actually paying that amount. This is based in part on encountering many stories of kids who thought they had gotten a promise to pay, got excited when admitted, and then were belatedly told by their parents they would not pay that amount for that school.
Generally, I note that among the savvy premed families I know, many choose colleges which are not the most selective their kid could get into, but they have all the characteristics they need and are relatively affordable.
So many do in fact choose an in-state option. Others choose a private where they can get substantial merit. Case Western, for example, is a popular choice. Some also do liberal arts colleges, which can be excellent for premed, good experiences in general, and under the right circumstances offer a lot of merit. And so on.
Again there is often nothing wrong with just going in-state. But if you would like some alternatives to that, I would encourage you not to just focus on highly selective privates with little or no merit (although if need aid alone would be enough, you can include some).