I'm going to have to come back to this because I did exactly what the OP is asking and picked up a cheap Chinese off-brand 7" for Barn the Younger. Specifically, I got the Prestigio PMP3570C, which is apparently not available anymore? Local here in KRK for about 320Zł.... so roughly a hundred bucks? And it was the best idea ever.

So first the drawbacks:
- It is not a Nexus 7. The screen is nowhere as nice to read, there's no GPS, it takes forever to pick up a signal from the router sometimes, and it won't stream HD from the DLNA server.
- It has "8Gb" of storage, but that's separated out into a too-small internal partition and an internal SD card. So for a few games that don't let you move to SD, that internal bit fills up fast. Then you can't install new stuff. Did not know that when I got it and this is the single factor that would make me wary of buying another one.
- It's fragile. BtY broke the screen within a week with a simple drop to the floor. Fixing it was almost as much as the tablet (which in hindsight was why I got a cheap tablet. I didn't want to fix the Nexus)! But now it's got a case and BtY is older - enough to know that you play with the tablet sitting down and don't walk around with it (usually). I think that's pretty good for a 2.5-year-old.
- The battery runs out even when it's in standby, faster than the Nexus. Not a big deal, since it's got not one but two charge methods, but it's still worse on battery. On the other hand, it does run a few days between charges due to low use, unlike the high-use nexus that needs daily charges.

Everything else about it is great. For a sub-$100 tablet I have no complaints. And watching BtY learn how the tablet works is incredible. Already mastered the task switcher, the home button, and swiping through homescreens. So far we've only got educational or pseudo-educational games and there's no complaints yet (BtY has no idea there's more games out there yet!).

So I could go on, but the first thing to ask is: Is this a tablet just to have a tablet, or do you want to spend a bit more to get something more substantial. How much is a Gen1 Nexus7? Because if you can get one for $150 (even a good used one) then I don't think it's a contest. Get the Gen1 Nexus7. That $50 premium over a cheap tablet is worth far more than $50. Updated to 4.3 it's a new device again. I've got half a mind to buy another one (or a Nexus10) for MrsBarn's Christmas present so she can read and mark up articles without having to have mountains of paper at home.

But if you can't get a used or cheap Gen1 Nexus7, then yes, consider a cheap off-brand tablet. I think you'll be mildly disappointed in some ways (especially if you go from a nexus to that on a regular basis), but in all the ways it probably matters (useable, portable, can put on games) it's going to be great.