We spent the day in Canada Park which is a national park in central Israel. The park had a small entrance fee (if you are not a member) but provided plenty of space for barbecue and lots of shade from the sun. They had beautiful trails both for bicycles and foot. The park was fairly clean and appeared to be well kept (this is not something to be taken for granted in Israel, I have seen really dirty parks with astronomical entrance fees). We visited during the week, however it was a holiday so the park was pretty crowded. They had toilets and wooded picnic areas. We brought our own food and barbecued with friends.