Sounds good looks like you have plenty of room to do everything you need.

That said not enough info and the plan is not indicating what is what, or what type of furniture you have for a tv room, what you need or have for the kid's play area, as toy storage goes you can frame a closet, you can use toy storage bins or organizers, etc.

You're dealing with one area find a wall to put a tv and set up the seating so it doesn't interfere with the access doors and passage ways, you would probably want to separate the play area from the tv area so you can watch tv while kids play without blasting the sound, etc.

This is the actual floor plan of the basement. I was wondering about play area under windows and tv on the opposite wall or maybe the back of the bathroom/bedroom wall.

We have a couch and love seat but maybe a sectional would be better?

This hasn’t been finished before- my kids have played hockey down there and still will. We will have to purchase a toy organizer to hide all the nerf guns, sticks, balls, dolls, lego, etc.

I see you have 2 bedrooms with fixed casement windows. To meet egress code these windows must be operable and cannot be fixed, they intended for escape and rescue.

R310.1 Emergency Escape and Rescue Opening Required

Every sleeping room shall have not less than one operable emergency escape and rescue opening. Where basements contain one or more sleeping rooms, an emergency escape and rescue opening shall be required in each sleeping room. Emergency escape and rescue openings shall open directly into a public way, or to a yard or court that opens to a public way.

R310.1.1 Operational Constraints and Opening Control Devices

Emergency escape and rescue openings shall be operational from the inside of the room without the use of keys, tools, or special knowledge. Window opening control devices on windows serving as a required emergency escape and rescue opening shall comply with ASTM F2090.

Oh yes. All windows are above ground and open.

All of those windows say fixed in the plan so you better check that. As for the layout of the large space could you not have patio doors instead of windows on that window wall if this is possible it would make the space feel so much better. Again all those windows are also fixed I like to be able to open windows for fresh air for sure. IMO closed storage for toys is great since this is also your TV space it is nice to be able to have adults there without toys every where. Who will be using the bedrooms? How old are the kids ? What do they need for playing in the space? You need to provide mor einfo.

No they say fixed/casement- half of the window is fixed the other half is casement. There are two windows in the rec room that are fixed. I built it. I live here.
This is a basement. 4ft in the ground. 9 ft ceilings.

Toys tucked away is a good idea. Maybe under the stairs would work? Use that awkward space?

Kids are 10, 6 and 2.5. They play mini sticks (hockey), nerf guns, lego, farm, ride on cars, hot wheels.