Like you, I try to keep the main floor looking nice most of the time (in other words- no random toys). My kids' bedrooms are upstairs and that's where they keep toys that are fragile or special to them. Our playroom is in the basement right off the kitchen/ greatroom. But when my kids were younger (your dd2's age I had a large wicker chest that I always kept some toys in. It was our coffee table in the last 2 houses. This "toy box" worked great for the toddler toys that didn't have a lot of parts. I didn't keep all our toddler toys in there. Just a few that I'd rotate out every few month with some from the basement. I'd never fill it completely full of toys. That way, if guests come by unexpectedly, there was still room for additional random toys and blankies and other stuff the kids dragged out. At one point, when the twins were toddlers, I had a second wicker box in the room.
" I object to violence because when it appears to do good, the good is only temporary; the evil it does is permanent." Mahatma Gandhi
"This is the ultimate weakness of violence: It multiplies evil and violence in the universe. It doesn't solve any problems." Martin Luther King, Jr.