Assuming, as we are (Kent is always right on with his ID's) that they are an annual sunflower, my advice would be to leave them be until the end of summer BUT by all means cut off any flowers that are spent before they spread any more seeds!
Since you really can't lay sod or seed a new lawn until fall anyway, (it's too hot) leaving them to be pretty for another month or two will prevent you from having to weed and mow what comes up if you remove them.
When it's time to get rid of them to make your lawn, I'd water generously, then pull them all. I mean, if you sprayed them or cut them down, you'd still have to get rid of the dead stems and root systems anyway. They'll be pretty easy to remove if the ground is moist. I had a stand of annual sunflowers as an experiment last year, and they came out easily, even standing 9ft. tall.
You could possibly hire a couple of local teenagers to do the pulling for you, too. I'd advise you to offer them a flat rate to do the whole job, though. Offering an hourly rate just makes them work more slowly. (from much experience here, too!)
All that being said, if it were my yard, I would just clear a small area near the house for lawn (if you must have some lawn) and leave a generous border for the sunflowers to come back next year. It looks to me as if they are providing you with some nice privacy from the neighbors right now and are also much more low maintenance than a lawn will be.
It's an outdated notion that a gracious garden must have lawn. It's very costly and work-intensive to grow, and everything you have to do to make it grow is bad for the environment as well. Mowing, watering, fertilizer, weed killer, fungicide, bug killer plus the cost of the equipment to mow and edge. Not for me! I have no lawn inside my fence, and my neighbor mows the weedy verges of the road for me with his rider mower in exchange for free well water.
