Hugh Taylor Birch State Park aka Birch State Park, Fort Lauderdale Beach

Directions:  Highway I-95 to Fort Lauderdale, Exit Sunrise Blvd. Head East towards the beach.  Just before you hit the beach it will be located on the North (left) side of the Street

Trail Information:   It's about a 2 mile trail through the state park and it's the only one I know of in East Fort Lauderdale.  The trail is pretty flat, grassy in parts and packed dirt in others.  There's a bunch of spiders (and webs) so keep your eyes open  :-)
It is part of an exercise parcourse which has 20 different stops, jumping logs, parallel bars to hand walk, etc...  It's not a long course but is cooler than running in the direct sun on the beach.  Parts of the course are along the Intracoastal Waterway which is nice.  Also, there's some wildlife: rabbits, boxer & snapper turtles, raccoons and parrots.
There are 2 water fountains in the park and plenty of restaurants and cafe's nearby.    

Miscellaneous Information:  If you walk in the park there is a $1 admission fee.  If you drive it's $3 or $3.50.  I suggest parking on the street (A1A) next to the beach and you can walk in, then you can run down the beach before or afterwards.  Bring your suit and jump in the water for a great cool off. 
Deborah London