No. It is more important to pick a daycare that is reputible, has trained personnel, and provides a safe nurturing environment for the child. Convenience, price and such factors are important, but secondary when decisions are made.
Yes. This is not a yes or no question, but depends on a parent's preferences. If a parent picks a daycare closer to work, then he/she can check on the child during the workday (if there is a question at the daycare, or if the parent just wants to check the child), and still return to work.
Yes. The quality of a daycare is much more important than its location. Pick the daycare of the highest quality, and then think about the proximity to work or home.
Yes. Your office. If there is an emergency at the daycare center, it's best to have a short trip from your office.