If I close on a mortgage on june 2 when will my first payment be due?

There are 2 possible answers to this question if you are referring to a 1st mortgage - July or August. It will be July if you choose to take an "interest credit" at the time of closing. It will be August it you choose to pay the interest due during the month of June at the time of closing. Your loan officer should be able to outline each of these scenarios with specifics to your mortgage and show you the difference between each of the options.

August 1st!

Jim gave a great answer previously. You should really be able to ask that question of your lender and know how they have it set up.

That's up to you and when you want the first payment to come due. If you take an interest credit at closing the first payment will come due July 1st. If you don't then you will pay interest at closing until the end of June and the first payment will be August 1st.

August 1st

Unless you specify otherwise, the first payment will be due on August 1.

Normally, it's the 1st of the month after the month in which the loan closes, but sometimes when that occurs in the 1st few days of a month, it's the the first of the next month. You will wind up paying the same amount regardless of when the 1st payment is.

It will be due August 1st unless your lender allows you to request it to be July. A first payment in July would mean lower pre-paid expenses than if it were in August.