As Walshey points out, except for Mississippi Kite, which seems to be easier to find in NW FLorida, you should be able to find some mentioned above plus others by checking a variety of habitats without traveling so far from your home base in Orlando.
Sharp-shinned and Cooper's Hawks are woodland and edge species, Harrier and American Kestrel are open fields or marshland birds, Osprey will be hard NOT to see in either fresh or brackish water habitats. Red-shouldered Hawk is best found in wooded swampland. Even Peregrines should be migrating through in April, more likely along either coast. Red-tailed Hawk is also resident. Watch for kettling Turkey and Black Vultures as other raptors often join them in the morning thermals.
EBird is an effective tool for pinpointing likely areas. For instance, Lake Apopka Loop Trail (17 miles from Orlando) lists Bald Eagle, both Vultures, Red-shouldered Hawk, Red-tailed Hawk, Swallow-tailed Kite and Osprey for April. Joe Overstreet Landing, on the east side of Lake Kissimmee (50 miles), lists Crested Caracara, both Vultures, Osprey, Bald Eagle, Red-shouldered Hawk, Northern Harrier, Swallow-tailed Kite and Snail Kite.
Steve