And the cabinets over/around the stove are exactly shaped for putting a microwave there, so it should be easy to install. So that's my plan.
Do you have an outlet there? If you plan to run it off of the range circuit check to see what else is running on that circuit first. Microwaves pretty much max out a 15A circuit, ranges use almost no electricity so you might find that your fridge is running off of the same circuit and you'll be popping fuses like popcorn.