What are you ultimately planning on for furniture? Will there be a TV?

Yeah, you sort of need to decide what the functional zones are here before placing the fireplace. Maybe you use the two arms of the L for different things -- one a cozy seating area around the fire, and the other for TV or games or desk work or whatever. Then the suggested placement would be fine.

If you want to gather around the FP, don't put it in the corner. Consider tricking out that wall where the electrical panels are as a complete built-in unit for books, decor and games and put a family game table in front of it. Put the TV where the outlet is under the photos or on the stairwell wall if the other end is to be an office.

If the gas line is already plumbed, doesn’t the fireplace have to be near the gas supply? That would make sense to me.

Yeah, what felizlady and acm said.

Thank you all for your helpful thoughts.

The gas is plumbed to the exterior wall near the electrical panels but can be extended to go where needed.

I would like the room to have 2 zones. 1 - more less an office space including a desk, the book shelves and storage cabinet, and the table. 2 - a family room area

I would like the fireplace to be a spot for gathering. There will be a tv above the fireplace. We already have a media room so the tv won't be the main focal point of this room. I want the room to feel cozy and inviting, a place to relax and have long conversations.

http://s1277.photobucket.com/user/treeshouse/library/Basement?sort=6&page=1

I installed our basement fireplace below the HVAC ducts running down the center of the basement. Ours is electric. Friends with gas units in their basements can’t enjoy them. Too much heat! Electric allows us to have the ambience with or without heat.

OP, the gas line may be able to be routed wherever, but remember that a gas fireplace also needs to be vented and the venting can only run so far/with so many turns in it.

Also want to echo the comment above. In a space this small with these low ceilings, it will likely get too hot with a gas fire. If you like the look of real flame instead of the sometimes cheesy looking electric, consider ethanol fireplaces. No venting or gas required, clean burning ethanol only. Still puts off heat but not as much as gas.

The room is almost 450 sq ft and the ceilings are 8ft - not as small as the pictures would make it appear. The fireplace would either be on an outside wall or directly beside an outside wall so venting would require many turns or distance. We live in the north where winter is long and cold so the heat is welcome not a deterrent.