I did my undergrad at ASU. I considered going for a MS after I graduated, but decided to work instead (I later went back for a MS in Electrical Engineering and am currently working on my PhD). I would advise against it, at least right out of school.
The ChE MS coursework consists of three core classes, Thermo, reactor design, and transport. The rest of your classes, the "technical electives," are taken from other departments. For example, if you are into solar energy, you might take a solid state physics course and a solar cells manufacturing course from the EE department. If you are into the bio-side of things you would look into a course in the BME department. If you like more the managerial stuff you will take finance, data analysis, and Six Sigma courses from the IEE department.
ASU has worked really hard the last few years on securing a lot of federal funding for large research projects (particularly in sustainable energy). Because of that they do have some top notch faculty teaching the grad level courses. In my experience the quality of the courses at the grad level is very high, so give it a +1 for that.
In addition to the coursework, you have to do an applied project or a thesis (which really end up being pretty close to the same thing). Your first semester you'll spend a lot of time begging professors to give you a project to work on. Depending on your personality this may be very easy or very difficult. Maybe you get something you are interested in, maybe not.
As you can tell, in grad school you really have to forge your own path. You pick your courses, you design your project. It's up to you to make sure what you are doing is worth the time and money you are putting in it.
How do you know if it's worth the time and money?
YOU DON'T!!!
If your goal is to be a valuable employee and make the big $$$ you need a solid understanding of what the industry you work in is looking for. You can only learn that by working there.
There is a lot you can learn in graduate school and it can be valuable, but you need to target specific areas you want to focus in. Taking a bunch of general engineering classes is totally worthless to a potential employer.
Here was my path if your interested:
After graduation I started working for a semiconductor company. I worked as an equipment and process engineer for 4 years and got a lot of great experience. I was able to work with guys who were industry leaders and came to the conclusion that if I wanted to succeed in semiconductors I needed to understand solid state physics in addition to process engineering.
I looked at the grad coursework offered by ASU and signed up for classes that specifically addressed topics I knew would be valuable
I identified professors that were doing research related to my industry experience. Because of my experience, my research advisor paid my tuition and gave me a second year PhD level stipend to work in her lab for my thesis.
Because I took courses and conducted research I knew was valuable, I had no problem getting internships during the summer that paid $40 to $45 an hour and continued during the school year part time
Since I was genuinely interested in the classes I was taking, they were a breeze. I was an average undergrad student (3.6) but I finished with a 4.0 in a totally different field because I loved the topics.
ASU is a great school and MS degrees can be beneficial to your career, but you have to play your cards right.
Hopefully that all makes sense. Feel free to PM me if you want more info.