I live here!
As far as parks go, West Malvern is lovely but quite difficult to find. (Look fir Old Hollow on a map, the park is up a track off Old Hollow near a small parking area on the side of the road.
Most tourists go to British Cap, but beware, the Malvern Hills Hotel is not child friendly.
I would massively recommend the Brewer's Arms, West Malvern as a spot for some lunch, then up the hills from there, or park near the clock tower and walk over to the Brewers.
The Kettle Sings is a nice cafe on the hills-ish.
When are you going? On Sundays, in the Winter Gardens in the summer (at 2pm I think or maybe 12???) There is always a band playing in the bandstand. There is a nice playpark there too (but no swings) and ducks in the ponds/stream.
Is it eating places, parks or something else you are looking for? Clives Fruit Farm, near Upton has animals etc. to look at. Let me know more details and I'll be able to help.