The longest lines are always for the antique cars - do them first before the crowds show up or at lunch time. Also they have a version of the teacups that tends to have long lines as well.
If you are staying anywhere you have to go south on Route 16 at closing time, expect to sit in traffic for a long, long time. Or go north from Storyland, turn left onto Glen Ledge Road at the Exxon station, when you get to the end of Glen Ledge, turn left again and you are on Jericho Road. It will take you back to Route 302. Turn left and you are headed toward North Conway. Also, if you are headed into North Conway, traffic will back up seriously going in to town. Turn left at the scenic vista onto Hurricane Mt Road. Turn right onto Kearsarge. At the first stop sign turn right again. You will end up back on Rte 16 in town but past the light where traffic backs up the worst.
You can leave the park and have lunch or you can bring a picnic. Food is OK at the park. The pizza is very blah.
Plan to get wet on Bamboo Chutes (a log flume ride) and Dr. Geysers wild raft ride. There is also a play area called Oceans of Fun Sprayground that the kids can get wet at.
Don't plan to eat at a nearby restaurant right at Storyland closing time. They will be packed with tired, hungry children!
Its a fun place to take kids. You can easily do it all in a day but if it works out, the PP is correct that if you arrive after 3 the next day is free. Saturday is the busiest day of the week. Most attractions run in the rain, unless we have thunderstorms or torrential downpours like earlier this summer. The exception is the Polar Coaster - a mini-roller coaster.
If you have any other questions, let me know.