The Heard Museum is a lovely museum in the heart of Phoenix. I recently enjoyed the Rick Bartow exhibit (exquisite) here, as well as Kahlo and Rivera. We also attended a docent-led tour and quite enjoyed the added information.
The Courtyard Cafe is great for drinks and a meal before/after or as a break during your museum visit.
Check the website for ways to get discounted admissions, e.g., Culture Pass, AAA, BofA, Blue Star Museums for military families, NARM...