I don't know anything about the Nexus so I can't comment on that but I have a Nook tablet and I love love love it!! I do need to be online to download books, apps and movies, but once the download is complete it's in the memory and I can access it any time. My Nook also has a slot for an SD card so if I can download it onto my computer then move it to the SD card I can access it on my Nook. Things like Netflix or Hulu you need internet for no matter what type of tablet you have.
As far as free stuff. There's a ton of it out there. I have 250+ books and I've paid for maybe 5 of them, and the most expensive one was $4.99.
Barnes and Noble has Free Fridays. They're usually adult level, but sometimes they have young reader options. Plus you can search for free books on their website. They also have a great assortment of complete works by specific authors, and collections of classics ie; Adventure classics, collections of Fairy tails etc...Many of those are only 99 cents for the entire collection. The complete Grimm's fairy tales is over 5000 pages and was 99 cents.
Also try Smashwords.com. That site is for people who self publish though, so you won't get anything mainstream.
http://www.gutenberg.org is a site that has older books that are no longer under copyright protection. ALL the books on this site are free, but as I don't have young kids I don't know what the selection will be for them. Also I don't know if you can load them right onto your tablet. I have to use my SD card for these.
If you have pinterest try this page: http://pinterest.com/mizpiggy/nook-freebies/. All of the books on it were free at the time of posting, so if you can access Barnes and Noble this is a great resource.
I can tell you for sure that I'll be checking back on this post to see what other sites everyone else recommends to you because I'm sure there are many more out there.
Happy reading :)