Your garden does need some plants. You can add some small trees like Amelanchier, Rowan, Hawthorn or Crab Apple, as well as some shrubs like Viburnum, Lilac, Ceanothus, Hibiscus etc. All very easy to care for once the initial post planting watering is done. You have a lovely big lawn for the children to play on but you could add a wooden climbing frame at the bottom along with a teepee or a summerhouse maybe? Lots of potential.

An idea of how old your children are and what type of play things you need would be helpful. Are you talking play equipment - swing / slide, trampoline, football goal, playhouse, sandpit, etc? Or just space for them to play? My preference would be for natural play where ch can use their imagination in which case I’d plant some small trees and shrubs that they could run in and around / hide, etc. The tree stumps type of equipment suggested by Sonia would be great for jumping around on. A planting patch / raised bed might be good to get them interested in growing. A small pond (if children are at a safe enough age) is always fascinating for children. This type of thing also incorporates the play into the whole garden rather than separating off an area, which in a few years might need to be changed. You could incorporate a couple of seating areas - shady under a small tree and a sunny patio. Depends on what you’re after really.

A lovely blank flat canvas. Small trees and shrubs would be easy to care for once established and don't require much maintenance. Having had to start from scratch myself the sooner you plant them the better. Houzz has loads of inspiration.