As for Jerusalem, I couldn’t figure from the website where exactly does the tour takes you but if you have time to visit the welling wall tunnels than I think it is really interesting. I do recommend you to spend a night in Jerusalem since the view of the lighted old town walls is amazing.
If you will spend a night there, I highly recommend you to have a glass of win at the wine bar on top of the noter-dam hotel : https://www.notredamecenter.org/ The view from there will be something you will not forget.
Make sure you eat Humus in one of those two places:
1 Arafat Hummus – Shuk ha-Basamim St, Jerusalem
2 Akramwai – near damascus gate
Don’t let your tour guide to take you to eat at Lina Humus or Abu Shukri. it’s Horrible!
Try also to visit the Mahne Yehuda market where you can find great restaurants during the day and great bats during the night.
I recommend to eat at Azura during the day – https://www.tripadvisor.ch/Restaurant_Review-g293983-d2526073-Reviews-Azura-Jerusalem_Jerusalem_District.html and at night to eat the the Yudale Bar at the market : https://www.tripadvisor.ch/Restaurant_Review-g293983-d5260216-Reviews-Yudale-Jerusalem_Jerusalem_District.html
You should also taste Israeli beers (there is a great store at the market) and a sweet thing called Rogalah which you will find at the market at a store name martzipan : https://www.tripadvisor.ch/Restaurant_Review-g293983-d7724827-Reviews-Marzipan_Bakery-Jerusalem_Jerusalem_District.html – that is a great gift to bring back home.
Other good restaurants in Jerusalem are Talbia wine bar near the Jerusalem Theatre, Hasadna and Mahne Yehuda – https://www.machneyuda.co.il/homepage
If you like meet you should also try to eat a dish called “Meorav Yerushalmi” at Agripas st. (near the Mahne Yehuda market) at a place called “Hatzot”. http://www.hatzot.co.il/ – it’s inner stuff but it’s really delicious. Take the one in the Pita for take away.
You should also try kibe at Mordoch on Agripas st. and an ice cream at a place called Muselin, right next to Mordoch. It’s sooo good!
Fix price / cash airport to hotel Shekel 170
Here are a few recommendations for place to eat in Tel Aviv (I warn you in advance, they are not cheap):
http://www.zeprarest.co.il/en/ – you need to book it in advance – Asian
http://www.hotelmontefiore.co.il/restaurant – you need to book it in advance – Chef
Shabtai Hayafe – Fresh fish – HaTsorfim St 36, Tel Aviv-Yafo, Israel – no need to book in advance
I recommend to go out at night at Jaffa area or Rothschild Boulevard.
You can easily take a bus to Jerusalem from Tel Aviv and take the tram to the city center or the old town. There are buses almost every 10 minutes and you can take them from the central station (not recommended) and from the Arlozorov bus station which located near the Arlozorov train station. I find this one nicer.