Dubrovnik with 2 kids under 10?

Dubrovnik's closest train station is a 4 hour bus ride away in Split. You should fly. Use kayak.com or skyscanner to find cheap flights.

I like Dubrovnik and it would be fun to stay there. There's also a lot of small towns nearby (one that's nice is Cavtat) but I enjoyed staying in Dubrovnik. There's a beach directly adjacent to the old town area. We're not beach people so we didn't try swimming there. If you have an entire week, you definitely have time for 2 or even 3 nice day trips. You'll have to do a little research to figure out which ones interest you and it will obviously depend on the interests of your children, as they're pretty young. We used this tour guide for two long day trips during our time in Dubrovnik. He'll help you plan trips or simply drive you around to places of your choosing. He's really great. He drives safely and his car is large enough for your entire family. http://www.dubrovnikrivieratours.com

We stayed in an apartment there. It was very inexpensive and quite nice. Right in the middle of town. It looks like it's about $90 per night now, but I think it's too small for you. It's perfect for 2 adults and 1 child but would be a tight fit for 4 people. https://www.flipkey.com/dubrovnik-condo-rentals/p227743/