I think towards the back would look better.

I would suggest putting the fire pit near the house since people will want to come in and out of the house. You could consider installing a stone patio so the fire pit looks like it's part of an outdoor entertaining area.

I agree with Elle, you want your fire pit on the patio where everyone is hanging out. I just did a design for a customer, with a similar setup like yours where deck stairs land onto a patio and they also want a fire pit. Here is an example to give you an idea.

Good luck

You'll want it close enough to the house to be reasonably convenient to the kitchen but not so close that there is even a hint of fire risk to the house or deck. Consider making the fire pit part of a patio.

https://s-media-cache-ak0.pinimg.com/236x/95/44/03/954403bbdf303686e9611b3f8f3d2cb1.jpg

You could even add a second set of steps from that last landing that turns toward the patio in addition to the steps toward front of the house and/or the driveway. You could also make beneath the deck a part of your patio set up to provide some shade.

If you want to be able to cook on the fire pit, you'll want it a bit higher; if you want it for heat for cool spring or fall evenings, you'll want it a bit lower to the ground but not actually in ground since that kind is more of a chore to empty out the ash, etc.

Making the fire pit walls wide enough to serve as a seat when not in use can prove useful when entertaining -- as long as no one sits on the side of the fire pit while it has flame in it and catches their clothes on fire.