We stayed in a rental home in Las Catalinas with our two girls ages 12 and 9. It is a beautiful Hill and beach town with 24 hr security and concierge service on Costa Rica’s northern Pacific Coast. There is a wonderful restaurant Lola's del Norte that we could walk to and they also have a Pura Vida Adventure shop to arrange side trips. I loved that I felt free to let my children explore the beach and village, and there was a playground in view from our gorgeous balcony. The home also had DSL internet access. The town is located on a cove so the water was very calm for most of our stay with people enjoying SUP from Pura Vida.

We shopped at the small grocery just down the gravel road from the town with super friendly people everywhere. We ended our Costa Rican stay at Las Catalina coming from Arenal which was only about 3+ hours away

Check out Manuel Antonio! It is touristy but not too over the top. You can find a long-term rental there for sure, there are tons of companies that rent houses by the month. The beach is beautiful and realxing, plus there is so much to see and do in the area (kayaking, ziplining, jet skiing, water fall visits, white water rafting etc). The town of Quepos about 5 minutes away has plenty of shops. The town of Manuel Antonio itself is essentially set on one hill. So you have Quepos at the bottom, the town of Manuel Antonio at the top and then the public beaches at the bottom in the south direction.
There are several great restaurants, shops, bakeries, a grocery store and a bank in Manuel Antonio.
It is about a 3 hour drive from San Jose, and you could take weekend trips up and down the coast to see other sites.
You could rent a car for the weekends only, it would definitely be cheaper. June has good rates too, typically a sedan costs about $35-$40 a day.

The Arenal Volcano is a must see for excursions, the Manuel Antonio National Park.. Corcovado is a beautiful remote place for camping, Tortuguero, Ballena National Park, the Poas Volcano, Montezuma.. those are just a few high lights there is a lot to see and do in Costa Rica!

Good luck planning your trip!

For must see places, I'd definitely say Manuel Antonio and the Arenal area with kids that age. If you're looking to go off the beaten path, the Osa and Tortuguero both have a lot of wildlife. I'd recommend trying to go the the La Paz Waterfall Gardens with the kids if you can. It's about an hour from SJO and has beautiful waterfalls, butterflies hatching, handfeeding of hummingbirds, etc. Kids love it. You could also see Poas volcano while you're in the area if it interests you. The only beach area we've visited is Manuel Antonio. The beach inside the park is gorgeous, and there is a lot of fairly tame wildlife, lots of restaurants, etc. We thought it was kind of pricey, so not sure if that area would fit your budget. If you can, I'd recommend staying someplace with some sort of security. Friends of ours rented a place, and it was broken into one night while they were home - not common but it can happen. And don't leave anything in your car unattended.

I will be traveling to Costa Rica this July to August for a little over a month with my two sons - ages 7 and 9. I have never been to Costa Rica, but I do plan on posting a trip report during my visit. We have enrolled in the Spanish Abroad Spanish immersion program in Tamarindo for 4 weeks, and will be staying with a host family during that time. We will also spend a week with my husband at the beach. I believe Tamarindo is very touristy, but it's where the program is based. After numerous hours of research, we have decided to visit Arenal and stay at Leaves and Lizards, as well as Monteverde and stay at the Monteverde Lodge. We will be renting a house near the beach at Playa Guiones in Nosara, which is supposed to be relatively quiet. We would have loved to visit Manuel Antonio and many other places, but we also want some time to relax with our host family. I have friends who recently traveled to Costa Rica, and they visited Tortuga Island and said it was beautiful.

I think that Manuel Antonio and Areal Areas are wonderful to your children,As a recommendation , I was in Costa Rica and enjoyed spectacular one day tours.
Costa Rica’s northern Pacific Coast is not expensive.
I am not sure about the rental car trouble, let ask one friend who rented a car during a month.
As I said , You do not have to miss the opportunity to get one day tour to Arenal, La fortuna, Caño Negro, Monteverde,Sarapiqui, Museums,ZOO, INBio Parque, Cahuita,Sarchi, Tortuguero, Marino Ballena National Park, Santa Teres beach.etc.
Check info about some One day tours: valledoradotours.cr/en/tours/one-day-tours.html
If you stay near to the beach, your children should take Spanish Lessons , During A month they can learn lot of vocabulary.