My betta always lays on the sand substrate around or on the leaves of my plants, he loves it like crazy. He'll hang out there for like 5 minutes and then swim away. He really loves the Java Fern I have substrate planted, and my two cryptocoryne parva plants that are on each side of the filter current, maybe he likes it cause the current goes against the glass and between the plants and he likes to rest there. It's his favorite spot, sometimes I swear he is dead in the tiny leaves cause he tangles himself in them LOL.
Finally got a pic (you can totally tell he is a double tail here ha!)