Wow, this is a difficult topic to tackle, because Alameda has many great parks. I'll list some for the geographical convenience and others for their stand-out features, or both.
Crown Beach can't be beat. There is a BIG parking, an abundance of picnic tables, lots of open space and a beach, of course. You won't find any slides or swings here, but then you have a real live beach. The beach is shallow with no waves worth mentioning. So little children can play in the water with supervision, but not constant concern for safety. There is a washing station to wash off the sand near the bathrooms. When everyone is hungry, there are grills available. Bring some jackets (it is sometimes cold), beach towels, sunscreen, hats, blankets for the ground, chairs, ice chests, charcoal briquettes, and don't forget your sand castle building supplies!
Littlejohn Parkis a cozy park located in central Alameda. It has a nice picnic area, big trees for shade, playground equipment, BBQ grills. What more do you need?
Washington Park also in central Alameda and it is BIG. You can find playground equipment, picnic tables and BBQ grills, basketball courts, tennis courts, and a dog park with separate areas for large and small dogs. It is right next to Crown Beach. You could spend all day here and not see the entire park.
Lincoln Park oh my gosh! I love this park. It is located on the east end of the main island. There is a parking lot you can enter from Fernside, if you must. But I much prefer to enter from High Street through the gorgeous gated entrance. Some pretty nice metal work there. However you get there you will find a rose garden, an expanse of lawn, lots of playground equipment, picnic tables and BBQ pits. There is a pool in the park that is run by a non-profit and requires membership to use the pool. So you can leave your swimsuits at home and enjoy all the other special features of this spacious park.
Tillman Park is on Bay Farm Island. I loved this park when my son was small. They have playground equipment, picnic tables, BBQs, ball courts and more.