I'm in this pickle right now.
Our 2005 Pilot that runs like a champ with 212k miles is all over the damn road if your holding it with 2 hands, just too much crash derby in that poor SUV - it'll be gone soon.
CRV, Pilot, RAV4 and Highlander will not be found in or near 10k unless they are very old, high mileage or a Salvage title.
Honda HRV however is really close and a solid little SUV, we have been looking at those closely. Don't count out a Kia or Hyundai, the right one will be cheap for a Teen to drive.
Lots of CIVIC Hatchbacks that are closer to 10k and will do the job.
The little Chevy GMC SUVs with the Ecotec are also solid if they are not beat up.
GLWTS - I'm doing the same.