Airbnb for apartment style: https://www.airbnb.com/
Hostelworld for hostels: https://www.hostelworld.com/
Booking.com for hotels: https://www.booking.com/
We recommend Tel-Aviv as your base point. If you plan on traveling the country it might be smart to figure out the nights you may be staying elsewhere in advance. You can usually leave your luggage at your Tel-Aviv hotel or hostel while you're gone.
There are many great locations in the city, however we encourage people to book their stay around Rothschild blvd. It offers tons of restaurants, bars and parties and it's central location makes it a walkable distance from many other spots in the city.
Airbnb is a great option! Make sure to take a look at the comments before booking. The city is very dense so apartments tend to be smaller than you think (imagine NY city apartments). We also highly recommend looking into hostels. There are some really great ones around!
If you are interested in hostels we recommend checking Hostelworld: https://www.hostelworld.com/
Abraham Hostel is one of the most well known hostels in Israel. They often have events and classes as well as live performances offered to their guests. The location is also great being close to Rothschild street where you'll find a ton of restaurants, bars and parties. While there are slightly cheaper options out there, this one offers a lot of experiences for a comfortable price.
They also offer family rooms of up to 6 beds which could be a great option for a group!
This is a chain and they have 2 other locations: one in Jerusalem and another stunning one in Nazareth.
If you are interested in a fancier option, there are numerous hotels around. We recommend checking Booking.com for hotels around Rothschild Blvd.