Cablevision Systems Corp. is pitching new packages aimed at cord-cutters that combine broadband service with a free digital antenna to pick up local television signals.

The move by the New York cable operator is meant to appeal to consumers who are tired of rising pay-TV bills and are dropping those connections. It comes just days after Cablevision rival Verizon Communications Inc. launched new low-price packages for its FiOS TV service that allow customers to mix and match tiers of channels covering various genres over a...