We have a play space near the window but just accept that toys are everywhere.
Kids want to play near their parents and play with their parents. I don't know, they love us or something.
Toys in the kitchen. Toys in the bathroom. Toys on the sofa. Toys at the dinner table. I accept it. This is a temporary phase of life.

Get used to toys being around so you don't drive yourselves crazy. We had ample storage in our old home to get toys away at the end of the day with area for play space. The reality is that DD wanted to cover the entire area at that age and it just made the most sense. Now with no storage, toys and art and crap all over the place. Get storage!

I would just choose a corner and look to Apartment Therapy or Pinterest for inspiration, e.g.:
http://www.apartmenttherapy.com/inspiration-tips-from-our-playrooms-a-roundup-177763

Also, would you want to designate the middle sitting room at the play room? Maybe not since there's a fireplace.

Do you have a basement? We put in "can" lights in the basement. Painted it white. Put in plush carpeting and turned it into a nice, safe play area. It's now the "study center" filled with books, desks, computers.

We have a cabinet and an ottoman that opens in the living room for toys. Its not a huge deal. I would make one of the living rooms a play room and close it off.

Use the sitting room as the living room and the living room as the playroom (so that the fireplace isn't in the playroom)?

Or in a corner of the living room, if it's big enough, use a separate rug or foam mats to designate the kid space, surrounded by shelving with drawers to contain the toys.

Float the couch in the front living room so that it faces the front wall of the house and acts as a "wall" dividing the living room from the family room. Angle chairs in towards the couch so it creates a sitting area.

Put a console or table behind the couch to store the toys.

Have the TV go in this room, add a kids table, bookshelves, whatever family room furniture you want.

We did this in 2 different houses. Second the bench/play chest idea. Your daughter is old enough to put her own toys away when she's done with them, so with some instruction about putting away one activity before beginning a new one, you'll get there.

toy chest that doubles as a bench

So, our new row house has a living room, middle sitting room with fireplace and then dining room next to galley kitchen, all fully open to one another. I'd like to allow dd (3) to have toys on the main floor, but right now that just means toys everywhere!!! Anyone manage to establish a play area in such an open environment? Any tips?