I usually don’t do that as my dogs don’t like to travel. I leave them with a family member or a pet sitter. Knowing that a reliable pet sitter would be taking care of the dogs, I can relax on a holiday.
I would suggest to check your neighborhood and ask the neighbours/passers-by if they had seen the dog. You may also report this to the authorities. You also need to think about what he likes and accordingly check for specific places like a nearby park, food store, etc.