Jeans or denim of any type are not allowed. Do not wear cargo shorts. Golfers don't, you shouldn't either. Dockers makes a nice selection of golf shorts as does Nike. Make sure they are comfortable and aren't too short. Wear a nice, clean, polo-shirt. Make sure the sleeves aren't too short. It's not a gun show.
Remember, golfers are CONSERVATIVE by nature, especially at the more prestigious clubs. Your attire should be too.
Tennis shoes would be fine but if you want to "fit in" head out and buy some golf shoes. Make sure they have soft spikes (non metal) and are clean.
