I graduated last June and am planning on moving to Fremont as a new grad NP. Where are the best residency programs for pediatrics specifically- and can anyone tell me more about them like pay, experience, competitiveness, etc?

That is something you need to research PRIOR to moving there. The best way is to find out how to be a preferred provider is to call the hospitals, find out what the pediatric programs are like, what medical insurance they take, then call those medical insurances and find out how to become a preferred provider. You will need your own malpractice insurance. Do Not rely on the hospital coverage, Your NP school should be able to give you the residency programs; make sure they have any openings in Freemont. You should have done all of this before you graduated.