It's a Chinquapin Oak (white oak family??). I don't think it would have much mill value as the process to take it down, because of close quarters, would require chopping it up into very small pieces for removal. Best I could hope for, considering the removal cost, would be to have a slab cut from the lower trunk to make a table.. a damn expensive one at that.
We also have a Black Walnut, about 70 ft. tall in the front yard. Right now the sucker is dropping bushels of nuts, been a bumper crop year I guess they are the size of lemons.