Even at 7'' you'll have trouble finding something at 1080p for that price, unless you're willing to buy used. Your best bet would probably be something like the Nexus 7, which would set you back between 200-250$. Google had a holiday sale on it for 230$, not sure if that's still available.
Otherwise, if you want to stay between the 100-150 price tag you will have to settle for a much, much lower resolution and definitely won't be able to go higher than 7 inches screen. I suggest you have a look at the Asus Memopad 7. Decent 720p screen, good brand although I'm not a huge fan of it myself. It's a budget tablet that is easy to recommend. You get what you pay for, don't expect a Retina display here, but for the price it does very...