The advice to go to Google Play is correct. That is the obvious first port of call for Android apps and there is a huge selection. Many are free, many are cheap and there are too many to choose from. Often you will find two versions of cheap apps, one free and one for about 65p. 65p is roughly equivalent to 99 cents US. The free version usually makes some money by displaying adverts. Get the "Pro" or "Premium" or "AdFree" version by buying it and you get rid of the annoyance of the adverts. Sometimes there are other benefits to getting the paid version, such as extra games levels or other facilities in non-game apps.
Much of what you can get is suitable for children and adults. You didn't say how old your kids are. The younger they are the more you need to look for specifically kids apps, but older kids like games and more games and there are lots of those.
There are other sources of apps, or appstores around. They have advantages and disadvantages. The biggest disadvantage is that an obscure appstore may have dodgy apps with malware on them. Hopefully other forum members will tack their own recommendations to the thread.
I think the other appstore you should consider after Google Play is Amazon Appstore at
www.amazon.co.uk/appstoreIt seems to run slow compared to Google Play. Not everyone has been happy with Amazon Appstore, but I am happy with it and I like their special offers. Amazon are trying to build up their market in Android apps so at present they are giving away apps that you normally have to pay for. Most of these are normally 65p apps, but some have bigger price tags. Many are games, and some seem aimed at a lower age group. Each is available for 24 hours, midnight to midnight, displayed at the top left hand corner of your tablet when you have the Amazon Appstore running on your tablet.
You won't save a lot on each Amazon offer normally, although one I got had a normal price of about £6. If you find a few you like the savings will mount up to a few quid. It is nice to be able to try out games and apps without the hassle of adverts running at the bottom of the screen.
John