Delaware LLC doing business in PA, NJ. Do I collect local sales tax?
Sales Tax is collected at the point of transaction, provided your company is physically operating in that state (or more widely, jurisdiction), or if your company has nexus in that state.
With that being said, I am not even sure your DJ services are taxable in terms of sales tax, you should check this question with your CPA. Usually sales tax is charged on tangible goods, but each state has its own tax peculiarities, so it's safer to get professional advise.
Keep in mind though, since you will be actively doing business in PA and NJ you might be creating strong nexus in those sttes, which means your Delaware company would need to file foreign entity in each of those states. Also, if you consider one of those state as your "home base" then you already create nexus in that state and would need to register the company there. Just FYI.