I work at Keymer pretty much every Wednesday, and try when time permits, to pop out from either there or Ditchling for an after work ride. The South Downs offers a brilliant range of terrain, all of which your bike could easily cope with.
Just three warnings though.
First... The bridleways away from the SD way offer more varied and interesting riding, but many are currently very overgrown with brambles and nettles.
Second... The chalk and flint sections can destroy tyres very quickly, and certainly cause punctures. This is made worse when conditions are wet. I've had one ride that destroyed three tubes completely beyond repair, back front and the spare. I've also had a major cut that destroyed a tyre when running tubeless as well.
Third warning... At this time of year, make sure that you wear sun block/cream, and also take plenty of water.
I don't record all of my rides on Strava, but you might find a few on here that cover that area. Example of most recent.
https://www.strava.com/activities/613351528
If you transport your bike by car, I personally think that Alfriston is a good starting point for rides on the SD. It's my preferred area of the Downs, and lovely rides can be had in either direction, with good opportunity for refreshment stops.
https://www.strava.com/activities/569607713
Friston forests also offers some very interesting ride routes.
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