How can I improve the garden to this house?

I would add a flower border to the lawn in the back yard, similar to the one you did on the front lawn. A big shady tree could also go on the back lawn, would be a good spot for a picnic blanket.

You could add a pool, and perhaps some kids playground equipment items. There could be an area for sims to grow plants to harvest. There could also be a firepit with seating.
These are just a few suggestions 🙂The home exterior design is very nice. 

That is a beautoful house!! You could always add some swing sets, pool/fouintain, planter boxes, greenhouse, flower arranging, or even a splash pad (pack depending) if not loads of greenary, trees and flowers, you can't go wrong!!! :D

When I'm ever in this situation, I just put kids stuff or planter boxes. Mainly I just scroll through the outdoor activities and see anything that seem like it fits. Also sometimes, I'll go for a pool to take up space without much effort or greenhouse if I have a green-thumbed sim (which i most often do). If your going for a minimalist/modern vibe, don't put anything and get a different tone grass terrain paint and make it look like a freshly mowed lawn.