As a tenant, you must pay a municipal tax (arnona). Each municipality requires a different amount for the tax. More expensive areas will usually pay a higher municipal tax. To get an idea of how much municipal tax you will have to pay, ask the previous tenants or your prospective neighbours.
Your landlord will ask you for a building maintenance fee (vad bayit). The more services you have (e.g. elevator), the higher the maintenance fee will be.
If you are a Jewish immigrant (oleh), you are entitled to subsidised rent up to six years after arriving in Israel. The Ministry of Construction and Housing will send you monthly payments of about 200 shekels for the first two years after immigrating. Payments for families can be up to 400 shekels per month. These rent subsidies decrease over time.