Suggestions?

The 2.5ish months that I am spending in Israel are my opportunity to see as many new things as possible. While I am using this experience to see if making aliyah (moving to Israel and getting citizenship) is something I want to pursue, I have no qualms about being a complete tourist. I want to get a feel for what normal life would be like, but I also want to see as much as possible.

This is where I need your help! I need to find a bunch of awesome places to go! However, I have certain time constraints:

During the month of June, my ulpan is 2:30pm-5:00pm on Sunday, Tuesday, and Thursday. I am also going to be taking a yoga class on Monday evenings. These are my only set things. This means that I can do day trips during the week and go on slightly longer excursions on the weekends. 

Here are the places I want to see:

~Cairo (duh)

~Petra (I think this would be a weekend trip, especially since I would need to start in Eilat, which is 5-5.5 hours away from Jerusalem)

~Haifa (I have never been here but really want to go! I was going to do a semester at the University of Haifa, but couldn't afford it.)

~Herzeliya (Maybe? I've never been and don't know too much about it.)

~Tel Aviv (I'm going to visit Ruthy while she is there, as well as a friend who lives in one of the suburbs...so I'm open to suggestions, but will probably go to my friend's favorite places or just wander around/check out bars/clubs with Ruthy.)

~Tiberias (I love Lake Kinneret. A lot. It's where I learned to skip stones. Also, as a native of Chicagoland, I'm a fan of lakes. My town has a beach and I spent my youth splashing in Lake Michigan. Also, I have eczema and salt water sometimes irritates it. Anyways, I want to take a trip to Lake Kinneret and Tiberias is a pretty interesting place.)

~Eilat (Since it's on the way to both Cairo and Petra, I'm going to be spending some time here. Even though it's technically a pit stop, I'll make sure to spend at least a day here. I'm not a big fan of Eilat, parts of it are somewhat tacky, like a mixture of Las Vegas and Miami Beach. But the Red Sea is awesome, and I can go snorkeling!)

That's all I have so far. I'm not a fan of the desert and Masada. I've been to Masada twice. Unless I go with my family or staff a tour group in the future, twice is enough for me. And while I love the north, I'm not sure what I would do there. Perhaps there are hiking trips? But since at least a few of these trips will need to take place during the week, I want to go to some places that are no more than three hours away.

Please, leave suggestions here or send me a message/post via Facebook!

And thanks!