Sit at home and play board games with your kids - not something that has bells, whistles, flashing lights, and beeps, but something where the mind has to be used, along with actual interactions between players, resulting in a few laughs along the way.
Create a project for you and your kids to work on TOGETHER for the summer. Maybe build bird houses or a dog house or maybe even a doll house with your little ones. Let them put in their ideas of how it should look and don't try to make it perfect. After all, some of the coolest things built with kids aren't perfect and contain a beauty all their own, uniquely and individually.
Set up a reading program or challenge if you have several children. Let them read at their own level, but entice them to read by you setting a good example and being part of it, too. Yes, make time to read with your kids and you can easily find that time by turning off the electronic gadgets that you've become so dependent upon. Those gadgets won't last, but the memories you create with your children will. And, if you're reading a fun, cozy mystery, go ahead and read some of it out loud to your kids, allowing them to read to you portions of the books they're reading, too. If your kids are too young to read, then set them on your lap and read to them, asking them what they see in the pictures. Point out different parts of what's talked about on the page, which hopefully is also reflected in the art work on the page.
If your kids don't like to read, then give them an incentive to do so. Don't ply them with the hope of a new gadget, but something they can learn from and appreciate - something like not having to clean their room for a couple of weeks if they read so many books. Or even better, having an Un-Birthday party at our local pizza joint, where all can join in and have fun; not just the children you have that were involved in the reading challenge --- but just don't tell them they'll get to all participate in that party, because they won't try to meet the challenge if you do. They won't put in the effort. Let the fact of them all being able to be at the party remain a surprise.
Work on arts and crafts projects WITH your kids. Don't just sit them in front of a bunch of stuff and tell them to make it - make it with them. One thing I found VERY enjoyable to make with my daughter was baking soda clay we would harden in the oven. She and I would then paint those creations we'd made and I still have several of those, as does she now that she's an adult and out of the nest. You can find recipes for making baking soda clay on the internet easily. Making this clay is fun, easy, and gives you an excuse to pull out cookie cutters you haven't used in years. It can also be molded into shapes, so let your kids imagination guide them and you'll have great works of art that will last much longer than the latest version of whatever stress-filled intelligent phone is currently being pushed.
Do have movie nights, but make those times adventures like I did with my own child WAAAYYY back in the day. Camp out on the living room floor or let them build a fort, and then you parents get into that fort with them. Let your hair down and let yourself be a kid again. Yes, you're the big people in the house, but there's no rule out there telling you that you can't reconnect with your children and play like them.
Turn off the phone and forget the junk you have to do at work. For a few hours, even forget the repairs and work you have to do on your own house or apartment. Forget the mounds of laundry and dishes in the sink. They'll wait, but your kids won't. Get outside with your kids and play ball or look at the clouds or stars, asking your kids what shapes they see in them. And, hey, maybe even ask them to make up a story about what they see in the shapes clouds and stars make (here is where I would suggest strongly you have a recording device hidden somewhere close, because some of the stories kids come up with are absolutely marvelous and so fun to listen to later).
If you have space - or even if you just have a patio/balcony type of thing - plant a little garden with your kids. What you sow today you will reap tomorrow applies in SO many different ways here. Let them see the fruits of their labors develop as they also develop patience. If it's too late in the season for you to plant things that would show up in the summer, then plant now that which will bear fruit in the fall. If you have limited space, try container gardening; there are many sites on the internet that will teach you how to do that and it IS fun.
There are so many things you can do to reconnect with your kids. Just turn off all the electronic stuff and be fully in the moment of enjoying time with them. They may balk at it at first, but don't give up; you ARE the big people in the room. So, if they sit back in the room and pout because they can't have their phones, start playing that board game or begin to build that fort yourself as you show them how much fun YOU are having - they'll usually join in just because they don't want to be left out.
Use this summer time to reconnect with your kids. Don't allow electronics to be their baby-sitters. Do stuff WITH your kids; not FOR them. Seriously, none of us know what tomorrow will bring, so make the time of Now count. You'll never regret it and the memories will last you and them a lifetime.