Think most of what I would want has already been mentioned, namely:
Proper food on the children's menu - my little boy won't eat beige and chips!
Everything done as quickly as possible - order taken, food brought, bill brought across, payment taken.
Nibbles whilst you're waiting for the food - this has been a lifesaver for us before. Literally stopped us getting up and walking out.
Plastic plates/cutlery/cups for the little ones - I don't want to spend half my meal wondering if the plate is going to break or he's going to have his eye out with the fork!
Freely available water
In theme parks etc, definitely cubicles that are big enough to take in the pram, and ones with specially adapted toilets/basins for little ones. If potties/toilet seats are available, they should be properly washed. I've seen ones with grime crusted on - nobody wants to sit their child on that!
Another one in toilets - free nappy bags! The amount of times we've had a disaster and I've only had the spare nappy and wipes I keep in my handbag, but no nappy bag to put the dirty stuff in. I don't like putting poopy nappies straight into the bin!
On holiday, free cots, highchairs, having baby gates available. I've specifically chosen resorts on this basis. Why are parents penalised for needing somewhere for their baby to sleep/sit? There are no supplements for a bed or a sofa!
The best welcomes we've had as a family have been from smaller businesses, where they can put the extra effort in.
With regards to a job in the industry, I suppose it would depend at what level. I would not discourage them from taking on a summer job, but I would not be encouraging them towards a career in hospitality - I've always felt it is under paid, unsociable hours and not conducive to family life unless you are senior management and can dictate your own hours. Anyone further down is expected to drop everything, including holidays, if there is a staffing issue. And this happens on a disproportionate level to other industries.