I think the easiest way to cull the list to is to cut the schools that are going to be above budget. Many of the most competitive schools only give need based awards so run the Net Price Calculator. If they aren’t affordable, don’t waste the application fee and the time.
If RPI is a serious contender, make sure that your son’s guidance counselor is aware. If he’s one of the top students at his HS, his counselor can nominate him for the RPI medal scholarship: The Rensselaer Medal | Admissions. That would bring tuition into your range and is guaranteed for 4 years.
Purdue’s tuition as is with no merit is also in your budget. Just be sure your son applies by the early action deadline so he can be eligible for honors college and merit awards, and priority for the his major. UMD is the same and there may be others, so make sure your son does his homework about deadlines.