If you are based in Tel Aviv then there is plenty for you to do and see in the surrounding areas.
For instance, just down the road is the marina in Herzliya. There you will find that they run a number of different events throughout the year including music festivals, beer gardens, special events on the beach and much more. Herzliya is a very short distance from Tel Aviv, and there are excellent public transport links.
If you are looking for a day trip away from the city then you can easily visit the city of Jerusalem. Jerusalem is only about an hour’s drive away from Tel Aviv, and there is excellent public transport links that basically run around the clock. In Jerusalem, you can visit a huge number of famous sites, such as the Western Wall and the Church of the Holy Sepulchre in the Old City, or the Israel Museum in the modern city.
One of Israel’s most famous attractions is the Dead Sea, and it is entirely possible to go on a day trip from Tel Aviv. At the Dead Sea you can bathe in the nutrient rich muds, float in the salty water, and also go to visit Masada, the famous mountain top fortress that dates back thousands of years.
In the opposite direction, you could go on a day trip to the Negev Desert in the south of the country. You can visit the old city of Beersheba (as well as the modern city), visit the local Bedouin communities, and even stay overnight in a Bedouin tent.
Geographically Israel is a very small country, so if you are based in Tel Aviv, then there are plenty of options for exploring outside of the city.