I'm not sure how the matchups are, but I find my least favorite opponents are ones with a really easy-to-land, strong grabs, might be because I like shield a bit too much. I find the tough matchups for me are Sonic, Sheik, Falcon, Diddy, Fox, maybe Shulk in speed mode? So far everyone else feels manageable, but this could just be personal experience.
Ness I find slightly annoying to fight, but if he goes for down throw fair, the second fair can get naired or airdodged into an aerial. Nair, down air and sometimes down B beat out his PK thunder if you hit the head, so that's nice for beating PK Thunder Spam. His fair seems to beat out Yoshi's in neutral, which isn't that fun, and eggs do well in that fight. Feels evenish to me.
DHD I like fighting with Yoshi. Egg hits can and it bounces the other way, and they can't lock down space with it the way they like. I've had moments where I got followups off a DHD's can into the pinball forward air up air stuff. Your air normals just feel a bit higher priority than his, and you're mobile enough to dance around frisbee and moustachedude. Watch out for smashes, but your shield is amazing. I feel Yoshi's got good tools for that fight.
Other, more experienced Yoshis will probly have more to say.