How exciting to go be going for your first visit
Regarding kashrut, best to speak to your rabbi what hechsherim he considers acceptable in Israel. Can get a bit tricky especially when travelling around the country.
Generally, the most accepted ones are eida chareidit, rav rubin and belz, but best to get a list and what symbols to look out for.
Definately must visit the kotel, the jewish quarter in the old city and generally just walk around and take in the holiness of Yerushalayim. The shuk at machaneh yehuda is also great but just need to know whats acceptable. If you get a chance also go up North to Tzfat, Tiveria etc. Beautiful up there and a lot of history.
As for beaches, there is a seperate one in Ashkelon, Tel aviv (specific days only) and at the dead sea.
Hope that helps