Driving from Amboise to Strasbourg

Troyes, you will love it.

It's not quite halfway, more like a third of the way, but look at the department of Yonne.
Auxerre, Avallon, Vezelay could be suitable cities for a stopover.
If you are a wine and food lover this is also an ideal place

In Auxerre you will find all kinds of accommodation such as the Mercure or Ibis hotel chains and even a Best Western Signature Collection hotel by the river and near the cathedral.

https://www.hotel-lemaxime.com/en/

Auxerre is about 2h30 from Amboise

About department of Yonne in general see:

https://www.tourisme-yonne.com/lyonne-en-bourgogne/les-tresors-de-lyonne/

Slightly out of the way, but if you can get a room, Perouges is unique and memorable. And it's much easier by car. The only hotel had a luxury cave room nearby, where we had breakfast with a view from our private patio.

Pérouges is near Lyon. The detour via Pérouges extends the journey by 350 km. It's not really "Slightly out of the way" on a french scale.

Another "vote" for Troyes. Stunning medieval town center, and lots of affordable accommodation.