McDonald's is spelled like that, with a capital "M," a capital "D," and no "a" between the "M" and "c." Most people would say, "Let's go to McDonald's" (no "a" before "McDonald's"), but there is nothing wrong with saying, "Let's go to a McDonald's," especially if there is more than one McDonald's restaurant to choose from in the area.
In that case, most people would not use "the." Most people would simply say, "Let's go to McDonald's." A visitor to your neighborhood might very well use "the," though: "Let's go to the McDonald's" --> "Let's go to the McDonald's in this area, which only has one McDonald's."
In the Santa Cruz area, there are at least two McDonald's restaurants. If I desired to eat at either of them, or knew anyone who did, I might say, "Let's go to the Mission Street McDonald's," or, "Let's go to the McDonald's at the Capitola Mall."
Otherwise, if it were understood which McDonald's we'd be going to if we went to a McDonald's, I would simply say, "Let's go to McDonald's." This is all hypothetical, of course. I never eat at McDonald's, and would never want to take anyone there.
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