My advice: Go with the flow. And: Divide and conquer, if you can. With kids from 1 to 5 there is quite a difference in what they can do and want to do. As a grandparent of five up to the age of 7 I have learned a few things about what they like. Just recently we were visiting two of them (6 & 3)and stayed our last night at a hotel near the airport (to catch an early flight). We found a place with a pool and had a pool and pizza party.
When they visit us during the summer, we take them to a playground, an outdoor pool, the beach (luckily near one), the zoo, a summer festival with children’s games and rides, or just set up the sprinkler, give them some squirt guns, and let them go at it. The older ones like to bike ride so I take them riding on the nearby trails or in the park. The younger ones love to push a toy stroller or cart up the sidewalk and explore. A soccer or other ball to throw and kick around can entertain and exercise them.
In the colder months, we look for a children’s museum, indoor kid’s play park, or children’s show or theatre (again for the older ones). A trip to the library is always in order. Many of them today have children’s programs (free!) and activities. They have computer stations with appropriate learning tools and games, puzzles, books to look at and movies to pick out. Almost every time our grandkids visit, we take them to the library.
Take them outside and play in the snow (a couple of them live in warmer climes and don’t get much snow, so to them it is a big treat). Inside, from about 2 years old on up they like to be “helpers”, so have them help you make pancakes, a pie or make and decorate cupcakes. Hold a scavenger hunt, and let them look for the things you hid in different places. Set up a “tent” and have a campout in the living room. Get some old clothes and accessories out and let them “dress up”.
You can also plan on special “girls” activities with just mom and “boys” activities with dad (or grandpa). It will make them feel special. Don’t discount biking as I did it with our kids and it is a favorite activity for our oldest grandchild. While the younger one slides, swings and climbs at the playground with grandma, the older one and I tool around on our bikes. Some kids are fascinated by airplanes taking off or fire trucks. Many communities have events where fire trucks and ambulances are on display for kids to see and climb on. Look for a cat, dog or horse show on a weekend, or an event with a petting zoo. Most kids love animals.
During the Christmas holidays, many malls and stores have special events and performances which appeal to children. Check those out.
I understand your concern about parks and playgrounds, but just be vigilant. The great majority of people there are just like you, parents or grandparents with little ones. I like the idea about finding an unused tennis court and letting them play in there, if necessary.
Also, ask other parents and grandparents in your area for ideas, just like you are doing here. Good luck.