Paper towels in the toilet as well as / instead of really loud hand driers - many small children hate these.
Yes - this!
As Vonklump says above, great service - which means making small accommodations for customers (eg making something that isn't actually on the menu but is a very simple combination of things that are on the menu - fish fingers with mashed potato, for example, rather than with chips).
As PP say - speed of service, plastic cups and plates, child-sized cutlery. Clear labelling of allergens. Antilop with tray. Very clean - preferably large - toilets. Nice waiters. Milk as an option rather than squash/juice. Low-priced set meals for dc.
Puzzle sheets etc are much appreciated by small dc.
Wetherspoons and Pizza Express are very family-friendly IME.
For hotels - the option of booking a standard double rather than a family room, when you have a co-sleeping toddler (with perhaps a small extra charge for breakfast). Usually there are only a few "family rooms" available, but if you don't actually need the extra bed this shouldn't be a problem.
For hotels generally it's all about getting the main things right (clean, attractive, great showers, great breakfasts, great service) and then the little touches on top that make you remember the place (fancy soaps, really nice china, butter curls).