Burlingame Park is a nice little neighborhood park. It would be REALLY nice if it weren't right next to I-5 (so it gets a bit loud). For us, it is walking distance and we frequent the park.
They have a playstructure that is geared towards slightly older kids (say 4 or 5...I am a little nervous about some of the features with my 21 month old, since they are a bit high). They do have lots of swings (2 for babies and 4 or 5 regular swings). Outside of the playstructure there is another big slide and a merry-go-round.
There is also a big field to play in and a baseball field and a tennis court (although today I noticed it was missing a net). There are also picnic tables.
If you are walking along SW Tail #4, you will go right through the park too.
We always bring a towel with us because with wet weather we dry things off, and today I noticed a lot of bird doo on everything that I was able to clean up before swinging and sliding.