I would second Nina’s place: High Point
Nice thing there to is for jumping you are close to other barns for jumping lessons…lots of hunter/jumper type barns on the south side of town.
Oh and Painted M also has stalls with runs attached.
There is another place too on the northwest edge: Stoney Meadows I don’t think there are trails very close but there are parks fairly close that do. She has a small indoor, some stalls with runs, and hosts a variety of clinics including jumping/eventing. www.stoneymeadows.com
As far as Twin Mills goes - I used to board there many moons ago but it has changed hands and I don’t know how things are going there…it is right next to Shawnee Mission Park so lots of trails there…it is pretty darn convientently located if the level of care is good…easy access from I-435 on the west side of town. I live about 2 miles from there and being close to I-435 gives me an easy drive into the city on I-70, easy access to the airport up I-435, and easy access to I-35 too. Shawnee Mission Park also has an awesome off leash dog park complete with swimming beach!
You should also keep in mind the drive…some areas are an easier drive in and out of the city and some are just a nightmare. This may determine where you want your barn to be and/or if you want to live close to the barn or closer to work.