I live in Webster and I'm sure you've looked at a map to see that we are northeast of the city of Rochester and we are bordered by Lake Ontario to the north and Irondequoit Bay to the west. In Webster, I recommend:
Webster Park (Lake Road at Holt Road) - take your kids to the rocky jetty on the lakeside of Lake Road and let them throw rocks and look for fish. There is a nice playground in the park too.
North Ponds Park - no swimming allowed but there's a nice paved walkway around the park. Public restrooms.
Bernie's Bouncers on Creek Street - indoor bounce house/playground.
Bayside Pub on Lake Road - go for lunch or dinner, sit outside and watch the ducks and swans. VERY casual local spot for boaters and fisherman (and everyone else enjoying a nice summer evening).
Friday nights at the town gazebo - free concerts and lots of kids dancing and parents enjoying the fun.
Webster Fireman's Carnival and Parade in July -
http://www.nejfd.org/content/webcarnival/
Webster Village Days in August - http://websterbid.com/village_days
Sunset at Hedges on Lake Road - go earlier for dinner and let the kids play on the nice big lawn right on the lake and watch the sunset with a cocktail.
http://www.hedgesninemilepoint.com/
Just across Irondequoit Bay in Irondequoit's Seabreeze neighborhood is Seabreeze, a family-owned smaller amusement park, perfect for kids your kids' ages. www.seabreeze.com
The zoo (Seneca Park Zoo) is also in Irondequoit on the city border.
If you want to take an adventure one day, head east on Lake Road, past lots of small fruit farm stands selling fabulous baked goods, to Sodus Point on Sodus Bay. www.greatsodusbay.org. It will take you about 45 minutes to get there. Sodus Point has a great beach and fun playground.
Let me know what specific questions you have and I'll try to help.