Either find a time when the park is empty (early in the morning?) or politely explain that you want to take a few family photos and will only be a few minutes.
Schools, Cityscape, even out in the country, stairways / archways, beaches or bodies of water, bridges, it just depends on your vision and what you want to do with the shoot.
Another idea would be a play on street photography or slice-of-life montage where you position yourselves within crowds of normal people and take photos that way (ie. waiting in line, crossing the street, having ice cream (kaito) or other favorite foods (banana, orange, leek, etc.), going shopping, playing at a video arcade, talking to or chatting with a public official or a bystander, and so on.