There are many apartments available VERY close to Ayala Mall, with the advantage of some cooking facilities provided (which can be useful, even if primarily dining out). Prices seem very reasonable. Booking.com is a good site to search for them - best to put 'Ayala Mall, Cebu' as search term and then you can filter using 'Distance'.
Red Planet, small room, but outstanding shower and very comfortable beds, there is a 7-11 downstairs and it’s right across the street from Ayala. 1500-2000 Pesos/night
Airbnb are the way to go, you pick the room, read the reviews, try to look for those that dont have cleaning fees, keep the cost down
Mandarin Plaza walking distance to Ayala. Free breakfast buffet. A very good recommendation. Check Agoda for discounts.
Depends on what you are lookin for... A year ago I found the Adelpha ( http://www.adelfahotel.com ), one block from old Chong Hua, two blocks to Osmena Circle (15 min walk to Ayala, not all that close). 1100 Pesos, very clean, very simple, tv works, no in-room safe, elevator always worked, door guard wasn't armed (if that's important to you), back room quiet but faces wall, front room some road noise, no restaurant, but, like I said, cheap. Stayed there a couple times......