Did you try that restaurant lately?
Did you go to that restaurant?
" You should use the present perfect, because you are talking about an action that occurred at an indefinite time in the past. "
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I would ask "Have you tried that restaurant lately?" and "Have you gone to that restaurant?" You should use the present perfect, because you are talking about an action that occurred at an indefinite time in the past. If someone were to ask me "Did you go to that restaurant?", I would probably reply with "When?"