On the weekends, it is generally true that you will not be able to stay at the base. This is because the soldiers that help you, (the Madrichot), normally go home on the weekends. This is not to be feared, but, an occasion for adventure. Traveling around most of Israel is pretty easy on the train and buses. Accommodations can be secured in Jerusalem and Tel Aviv, for around $40 or $50 a night, sometimes less. For those lacking in both funds and a sense of adventure, the Sar-El Hostel is available for free. Meals are provided at the hostel and they are along the same lines as what is served at the bases. The hostel is located in Old Joppa within walking distance to stores, shops and fast food, as well as the beach.
One neat thing about Sar EL is, that, you will find the "experienced volunteers" to be a wonderful assets who will help you with ideas for the weekend activities and destinations. Sometimes volunteers band together to share weekend accommodations and/or adventures. At any rate, your Madrichot will help you to make the necessary reservations. Scroll on down this page to see some of the interesting places you can go to on the weekends.
One word of caution, from Friday near sunset to Saturday, is the Sabbath and the majority of the country shuts down during this time, so, you should have a plan as to where you will be staying and what you will be eating. There are some restaurants where you can eat on the Sabbath but, the choices are limited and sometimes, difficult to find during the Sabbath. There are many great and wonderful things and places to see in Israel, below are just some of them. Here is also a link to a great site that will provide a lot of great information about the parks of Israel. National Parks Authority.