I have an upcoming trip to Crawley and will have a Saturday to myself at the end of the work week. I will have a rental car and prefer scenic sight-seeing country drives, etc, but am up to pretty much anything. What would be a recommended non-urban Must-See for the area (within 150km) if I only have a day?

Whatever you do, don't stay in Crawley. My family made the strange decision to move there from Edinburgh (luckily for me just as I was about to go to university). Crawley really has almost no redeeming features.

When I go home to visit, I tend to escape for day-trips - often London, but at other times I'll head down to Brighton for some lunch, interesting shopping or to watch Sussex play cricket.
Not sure what your definition of urban is, but I also like to visit Lewes which has some very interesting history. Other options (in a slightly different direction) would be Arundel or perhaps Chichester.

More rural thoughts? Beachy Head, walking the South Downs. I also like driving the back roads. Get off the A23 and there are some great little rural roads that have tree canopies over them in the summer. Get a convertible, put the top down and turn up the music. Oh, and hope it doesn't rain.

I would second all of captain schmidt's ideas.....

Brighton and Lewes can be a nice pairing..... also check out Seven Sisters and Beachy Head south east of Lewes on the coast....

Alternatively... if you are interested in actually visiting a few places and want a break from driving....

the following places are within an easy 1 hour drive of Crawley (mostly to the east) and I am sure you could find out more about them on the net and plan a route to link a few of them up. The scenery is pretty good around there whichever route you choose.... although sticking to the "B" roads (ususally yellow on the map) is usually better !!

Chartwell - Churchills Country Home - near Westerham (but check opening times)

Quebec House in Westerham also has a Canadian connection !!

Hever Castle - connection with Henry 8th - near Edenbridge

Chiddingstone Village - also near Edenbridge

The village of Hartfield - has a connection with Winnie the Pooh

Sheffield Park Garden can be stunning in Autumn

The Bluebell Railway (also at Sheffield Park) operates Steam Trains at weekends

Wakehurst Place - is an annex to Kew gardens

Errr, my fondness for sardonics notwithstanding, my first thought when reading the title of the original post was "run away quickly". The fact that I almost got mugged at Three Bridges might have something to do with it.

I'd head to leafy Sussex, the South Coast or to Tunbridge Wells to post an anonymous letter of general complaint to the Telegraph, for publication.

Wirelessly posted (Mozilla/5.0 (SymbianOS/9.1; U; en-us) AppleWebKit/413 (KHTML, like Gecko) Safari/413 es61i)

Beachy Head is lovely, best approached on foot, though, having walked thr Seven Sisters - plenty buses to get you back to the car park.

Otherwise, the South Downs are beautiful, as are the North Downs. You could walk along part of the long distance footpaths (North Downs Way, South Downs Way), stopping off at any particular highlights (Amberley chalk pits, St Martha's Church).