My 2 year old son woke up this morning with a limp. No injury. Not putting weight on left foot. Should I wait or take him to a doc or ER immediately?

12 hour rule. For toddler limps i typically temper it fairly mildly, trial tylenol (acetaminophen) or Ibuprofen and have the parent re-evaluate over the course of a day. Without fever or trauma history an attentive parent is unlikely to ignore to the point of negligence. Having a provider evaluate is certainly appropriate, but don't fear if they tell you that with that history a small waiting period is okay, staying off it.
Yes. Although many toddlers limp and are found to have benign causes that resolve rather quickly, i recommend an urgent evaluation with your pediatrician or an orthopedist to rule out a fracture, infection or something else requiring immediate attention.
Needs to see the doc. A child with a limp needs to be taken fairly seriously. It's typically not a bad thing but there are some very bad things that can show up initially as a limp. It's not necessarily worth an er visit but he should be seen as soon as possible. An urgent care visit today or same-day appointment wouldn't be unreasonable.
Depends. A kid sliding off a couch with heal outstretched can transfer enough impact to the hip joint to cause swelling overnight & cause a limp. If the kid has no fever & is otherwise ok, he can see his pcp on a space available. Limps can be caused by infection in joints or unrecognized trauma that could have cracked a bone. If febrile or uninterested in play or feeding, i would have it seen immediately.