Getting around Alexandria can be done easily using taxis, private cars, or public transportation (buses). Taxis and private cars will be more expensive but much more comfortable while the buses will be more affordable. If you plan on using taxis or private cars, be sure to agree on the prices before commencing the journey, while public buses are also reliable, the schedules may not be as flexible.
If you have more time, consider adding a visit to the Pompey's Pillar and Catacombs of Kom el-Shoqafa, both of which offer insight into the city's ancient past. If you have less time, consider skipping out on the Montazah Palace & Gardens.