My mother developed an allergy to sunscreen, and can’t use it any longer. My skin is somewhat sensitive. I have liked Simple Skincare Replenishing Rich Moisturizer - they have a formula without sunscreen (and one with). It’s light and inexpensive:
http://www.simpleskincare.com/our-products/product/replenishing-rich-moisturizer.html
I’m currently using Advanced Clinicals AHA, which I got at TJ Maxx for around $5: http://www.advancedclinicals.com/body/advanced-clinicals-alpha-hydroxy-acid-cream