Things that seem to entertain my kids the most in the yard: digging, rocks/sticks/bugs, throwing balls, bird watching, water play, bubbles, gardening. The only things I've purchased are a few kid sized garden tools, a kiddie pool, a few balls, a magnifying glass, sidewalk chalk, and a couple of bird feeders. We live near several parks.
DS2 naps a lot in an Ergo. It's not intentional on my part, but if he's in there long enough, he tends to pass out regardless of whether or not it's nap time. On really busy days, I take advantage of this tendency, but he will nap elsewhere.
Hate to say it but he sounds like pretty much every 4-year old boy I've ever known... Try to focus more on the positives--praise him when he gets it right, shows signs of maturity, thoughtfulness, etc. I find punishment other than natural consequences does not seem to help motivate change that much.