I don't think it's very informative to ask the schools themselves. While you can ask things like how many counselors work in their career services departments each school is going to tell you that their career services offerings are great, and teasing out useful information from these responses will be difficult. Instead I'd ask former students (since current students haven't actually applied for and gotten jobs for the most part), though since most students have nothing to compare their schools' career services to it can still be confusing. Many alumni are happy to chat if you reach out, in my experience.
Despite what I just said about current students, I can speak a bit about UCSD GPS' career services. I have found the department to be quite good, and a major draw for the program. GPS has three full-time and one part-time career counselors, which for a program of ~300 students is a good ratio and in my understanding higher than other international affairs programs (I can't speak to MPP programs). I've been able to have career services employees proofread resumes or hold mock interviews on very short notice, and they are usually available for one-on-one meetings within a few days. Each year career services hosts trips to the Bay Area, DC, and NYC (though at the students' expense) to visit employers, and are very involved in finding summer internships. Career services has good relationships with seemingly all Masters of International Affairs alumni (there are not yet MPP alumni at GPS), and will often reach out to alumni on students' behalf. Their advice is usually very good, though I've had employers give different feedback on resumes than career services
The quality of career services is only one part of getting a job of course (unfortunately alumni networks probably matter more), but my impression of GPS' has been good.
I'm currently looking at about 5 different grad schools for an MPP. I keep hearing (and reading here) that I should strongly consider what the career services for each school offer. For a professional degree like the MPP, it will be very helpful to have a strong career office at the school (and alumni group) that help place students in related careers. The thing is - how do I do that? What is the best way to compare or evaluate a school's career services offices? (Do I trust the school and call the admissions office? Or ask current students)
If any of you have any experience doing this, I'd love to hear it!
FYI I'm applying to these schools: UCSD, UCLA Luskin, USC Price, UC Berkeley Goldman, and UChicago Harris.