Bill Baggs is a state park at the southern tip of Key Biscayne. It includes beach access, walking trails (great for birding), a historic, mid-19th century lighthouse, and a couple bars and restaurants on the water. You can easily spend a day lounging on the beach, taking a tour of the lighthouse, and getting food and drinks on the water.
Crandon Park is a lovely, long beach on the north part of Key Biscayne. It's about a 25-minute walk from the Silver Sands hotel, or a 5-minute drive. There are a couple restaurants and/or food trucks there. You can combine a trip to Crandon Park with a stroll throught the Quiet Garden (formerly a zoo), which is just south of Crandon Park. Peacocks and other birds, iguanas, and turtles live in the Quiet Garden, and you might get lucky and see the resident crocodile, Chompy, on the shore by the pond. Crandon Park also has walking trails that lead all the way to the north tip of the island overlooking a fossilized reef, with a lovely view of downtown Miami.
If you want to explore Miami, there are plenty of places to visit. Miami Beach: Stroll along Lincoln Road, take in the art deco architecture, and visit the beach. Wynwood and the Design District: Visit the Wynwood Walls, browse art galleries, visit some great bars and restaurants, or go shopping in this artsy neighborhood of Miami. Coconut Grove: A low-key area of Miami with a nice little downtown area and some good restaurants and local dive bars. Little Havana/Calle Ocho: Get some great Cuban food, play some chess, or go dancing at Ball and Chain.