Ages of kids? Interests?
Hike up to Table Rock in either morning, or evening, to watch the sunrise/sunset can be fun. The Western Idaho Fair is in August.
Namely, each week there is Alive after 5 concert series downtown. There is also First Thursday (each month). Once we can get through all of the run-off and re-open the greenbelt, there will be random things in the parks, the zoo used to do a sleepover/Night at the Zoo event. Movies in the Park- Julia Davis Bandshell, or at Settlers Park in Meridian. Lots of people float the Boise, but I have a feeling it won't be available until August. Disc golf at Ann Morison. Do you have a GPS? Maybe go geocaching? Old Idaho Penitentiary, tons of museums. Go white water rafting up at Banks on the S. Fork of the Payette. Stand up paddle Boarding at the new Esther Simplot Park & Quinn's Pond. Once it gets hotter, if you're brave enough, go to the Boise River whitewater park and try surfing. Day trip up to Idaho City, go check out the World Center for Birds of Prey.
A lot of people like to be outside, so hiking, fishing, riding bicycles, camping, etc. All pretty easy to get to from here.
Here are some random links.
https://www.downtownboise.org/index.cfm/home
Idaho Military Museum
Idaho Geocachers
Boise Music Festival
Old Idaho Penitentiary
The Basque Museum
Movie Night Meridian
City of Boise Parks & Rec
Boise Visitor Guide
World Center for Birds of Prey
Warhawk Air Museum
MK Nature Center
Visit Idaho
I'm sure others might chime in. Give us some more details and we'll try to offer more help. Also, since you registered your vehicle, did you add the state Parks pass for $10? If you go to Eagle Island, Lucky Peak or any of the State Parks twice, it's paid for. If not, contact the DMV, tell them you recently relocated to Boise, but didn't know about it and see if you can get it. It's two little stickers that go on the outside of your windshield, about the size of the sticker that goes on your plates.