Applying for a new job and I need to know when it asks for my recent employers phone number do I put the store where I worked?

You put the corporate office. All they are allowed to tell is name, dates worked (start/end), and rate of pay. Nothing else is permitted by law. You can give references, which might include previous managers, but only if you've got their permission, they give their personal email and cell number. Anytime you change jobs, contact your references to make sure they know what you're up to, what you've been doing since you worked there last, etc.

The store you worked for and the manager are not supposed to be contacted when you apply for work. Most retail stores don't have time to give references, or employment details, and is against store policy to give out that information.

If the store is contacted, and they learn you're looking for another job, you may get close to 0 hours on the next schedule or they may write you off the current schedule also. It is always bad taste for your current employer to be contacted by a future employer, unless you've already given notice.

So they ask... what's the big deal?

At the very least you might get to leverage your job-seeking and make your current job more beneficial.

If they make it rough for you, what do you care, you are leaving...?

You put the store where you are working - they are the ones who can verify that you work there, your duties, etc.