I would strongly suggest looking for accredited programs - they should also be much easier to find than non-accredited ones.
For some fields, such as civil engineering it is absolutely essential. It can also be very important for most other fields.
Even if you don't care about getting jobs that require an accredited degree, you should be concerned about the quality of the program if it isn't accredited.
One exception to the above might be computer science. Even some highly regarded schools that have fully accredited engineering programs do not have accredited cs degrees (stanford, ucsd, cornell, u washington). In that case, though (especially since you aren't looking at a program with such stature), you should look at what kinds of jobs the graduates get.
What other options are you considering?
Jason
Edit: for what it is worth, I am an engineer who has been in industry for almost 20 years. To my knowledge, I've never worked with someone that has an unaccredited engineering degree. I have worked with folks that earned physics and math degrees that essentially work as engineers, but they have been hired for work that does not require the breadth and depth of a particular engineering discipline. If you want to do engineering work, you really should get an accredited engineering degree. There are many many schools that offer them