Take a friend - they'll be more motivated to do trips out if a mate is going.
Just walks are hard for kids. Research routes like country parks with playground, short walks in the country (2-3miles max) that take you via something fun to explore like caves/ruins/woods with good climbing trees/ streams you can paddle in.
If you know anyone with a tolerant dog arrange to borrow that for the odd walk.
As well as geocaching and Pokemon go download the seek app so you can identify any plants you see. Count birds, count bugs. Check out your local wildlife trust, they often have free events on for children in summer. Wherever you are there will be something amazing to see if you keep your eyes open.
Have a bag on hand with a basic first aid kit (not joking, walks are miserable after you have untreated nettle stings, insect bites etc), Sun cream, bottles of water, box of emergency Jaffa cakes and a small towel.
Focus on quality over distance covered. Did you get outside? Enjoy it? See anything interesting? The long game is giving your kids the confidence to enjoy getting out for life. Making them walk five miles with blisters is an excellent way to kill that off.
Don't worry about taking a book to the park. That sounds lovely. A walk to the park on a sunny day, chill out with a book, a picnic, maybe poke about looking for new wildflowers or new bugs or play Pokemon go. It's not the Olympics but it's building small bits of extra exercise into every day that will help them build healthy habits for life.