If you have a Ph.D. in engineering and they are interviewing you are in a strong position. There is a real shortage of Eng Ph.D's in the USA - especially ones with decent language skills.
Are you expected to do research, get grants etc - I suspect not - which ie good - that is a real pain.
Academic salaries in the US are really very low - which is why most Engineering faculty are not from the US.
Starting salaries for an Eng with a master degree are 45-60 K – even more if you are electrical etc.
Also ask about doing outside consulting - giving short courses etc can be very lucrative. Some places limit you to doing courses through the institution’s FE division. This is not good.
Outside consulting is often limited to so many hours per week or out of term. Again this can add up nicely. (Another issue is can you get back billed for using your office for outside work)
A lot of people really like AZ and the cost of living is low, ERU has a good reputation but I think it is real geared to produce airline people.
Unlike the UK company perks are not as common here and because of the lower taxation not such a big deal.
The general advice is never state a salary - let them offer and then don't say anything.
My guess is you should be looking toward the higher end of the associate range. They can only say no.