If you're planning a bit of sightseeing head to Monastery of Abu Mina— just one of the monuments located 25 mi (40.3 km) from the center of Alexandria.
Hostels can be a less expensive alternative to Dawwār al Ḩājj Khalīl hotels, as you can stay in a shared dormitory. There are 3 hostels in Dawwār al Ḩājj Khalīl. Alkadi Hotel offers free WiFi in public areas and a 24-hour front desk. MADEII project training center hostel has free WiFi in public areas and free parking. Caesar hostel is another low-cost option.
