Depends where and when you are going?
Note that its a muslim country, and whilst you don't need to cover your head, I wore conservative clothes (T-shirts, 3/4 sleeved blouses and at least knee length skirts or cullotes, long linen trousers) and no shorts when out of the hotel. Also no spaghetti tops. Even then, I was stared at no end! A light pashmina/scarf is handy if you do visit somewhere that requires a head covering, or shoulders covered.
My MIL came shopping with us 1 day, and thought the following outfit was acceptable: short shorts and a swimsuit (no bra and hadn't shaved any part of her body! No cardigan or cover at all). 
Generally the weather is hot and dry, so invest in cotton or linen, loose clothing in light colours. Nylon/polyester will just make you sweat. Comfortable trainers if you will be doing alot of walking, and comfy flip slops or sandals.
If you are going near Sinai peninsular, you might climb Mt Sinai. I cannot recall when we visited, not the height of summer, but also not in winter. We were told to wear warm clothes. At the bottom of the trek, which started in the very early hours, people were trying to sell us woolly hats, gloves, blankets etc and said there was snow on the top!!! We assumed this was purely a gimmick to sell tat to tourists. To our great suprise, after several hours of walking and at the top, there was indeed snow and ice all around and it was freezing. I had every piece of clothing I'd brought with me in multiple layers, and still had to buy gloves and a scarf!!! Nights in the desert can also be cool, so take a cardigan and scarf along.