I agree with above about telling him what you're going to do instead of asking. If you want to go on a walk/to the museum/library, whatever, just plan a time to go and tell him a bit before you leave and then when you're ready, that it's time to go to the wherever. My 3 year old is very fearful of humans and a wide variety of situations and if I'd ask her what she wants to do or whether she wants to go she would say no most of the time, but after we actually go she doesn't want to leave and later talks about having a great time. So I don't ask. At this age they are so bad at predicting how they will feel about anything, they truly don't know what will make them happy in the future
Try using his independent playtime as a reward for him completing other activities you want him to do. Start with small things first like "do a puzzle, then play. Work on letters, then play." I also sometimes decide on an activity for us to do. I will set up painting supplies, and we will paint for a bit just to get them used to attending to a requested task like they will have to in school. I say they because I have twins.