There are no hotels near the airport. TLV is located between Jerusalem and Tel-Aviv - it takes only about 20 minutes more to go from Jerusalem than Tel-Aviv so you don't want to waste hours changing hotels to save a few minutes. Your options from Jerusalem are a private taxi, the Nesher sherut (shuttle) or the 485 bus (doesn't run on the Sabbath). The sherut (a 10 seat minibus) picks you up at your accommodations and costs 67 NIS pp. The 485 bus leaves hourly from near the Central Bus Station and costs about 14 NIS. You can calculate the taxi fare here:
http://www.iaa.gov.il/en-US/airports/bengurion/Pages/TaxiFareCalculator.aspx