And, honestly, after your first job (or maybe after your first few jobs if you don't stay long at your first job), it really is mostly only a matter of curiosity where you went to school for any of your jobs.

Engineering is very much a performance-based career. It matters what you can do WAY more than where you went to school. If you are a good engineer, you will have plenty of opportunity in your career no matter where you went to school. (Although I will quickly add that who you know definitely matters in terms of getting that first job, so going somewhere where you will come out with a good network is an advantage.)