Limited to Arnhem 'gemeente' (council) only:
Lauwersgracht, Arnhem was the first city in Netherlands to be allowed to tear down city walls, parks were built with new districts built on the other side. After Napoléon was defeated, and before Belgium went independent this was.
Soon after van Heemstra acquired lands, built a Belvedére with money from his Paris friends helping him to extend the park; Sonsbeek: an exposition location, EU's #4 or so when with Kassel's Dokumenta as #1.
My fascination with skylines and tall buildings was developed on top of the top right building (only 11 storeys actually) when my father worked there and the then tallest in the country was built somewhere else in Arnhem. I recently found out about Highland Games being held at Sonsbeek Park

. It borders Zijpendaal:
www.mooigelderland.nl offers loads more. Yet not from the cricket played there.
further north and uphill:
I should specify: uphill is from some 35ft above sealevel upto 250-300 (and rising!) ft over a distance of just a few miles. Looking, for steep hills in this flat country, ought to lead you to the Arnhem area.
Outside of the city but still in the 'gemeente';
towards Oosterbeek (Hartenstein, Airborne, battle ground 1944)
Straight next to the Rhine, it's Bovenlangs and Onderlangs; one street uphill (former hospital, museum, station) with splendid views over Onderlangs, Art School with new Dance School in the subterranean building:
This ^spot is stunning; you're standing next to a great river, thousands of people do all arts except opera, even under the ground you're standing on. And if you still don't like it, Amsterdam's 64 minutes, Frankfurt 2:44hrs plus that little walk uphill, 5 minutes at the most. Across the Rhine, new parks were developed because Arnhem is not allowed to build urban parts any further along the Rhine. ***** have been put further away from the river, thus enabling a larger overflow of water, should it come. Like from melting snow on the Alps.
Meinerswijk (recently discovered ruins of a 9th century castle/fortress), the river is The Rhine. You'll find Scottish Highlander cows and bulls and modern art. Weird mixture!
Welsh dubbers Zion Train played this park in 2003: it marks the south border where you litereally smell Nijmegen (Weurt's power plant) already.
A terrible decision was taken. Presikhaaf mansion was torn down. This is the park:
So, that's your lot! Arnhem, like Kassel rates amongst the greatest park cities. I have excluded all the Burgers Zoo, Burgers Desert, Burgers Ocean and Burgers Safari plus Openluchtmuseum on purpose. Including neighbouring towns and villages would be overdoing. Should you want more: searches should read: Rosendael - Biljoen - Rhederoord - Middachten - Doorwerth - Doornenburg - Gelderse Toren - Bilderberg etc.