I don't have a dedicated playroom, either. So I converted a closet on my first floor by taking out the clothes rod and putting in a system with pull-out bins and shelving for toys. I'm pretty aggressive about weeding through the toys on a regular basis--even so, I still have overflow from the "toy closet." I bought a couple of big, attractive wicker baskets (the type you would store logs in by a fireplace) to handle the overflow. That way I can lug them around and just toss toys in when I'm tidying up at night.

Wicker trunks work great and they're not heavy enough to hurt little fingers. We've also used those cube-style ottomans with fully removable lids. If you're in the market for new living room tables, you can find coffee tables and end tables with shelves underneath that fit wicker baskets as well.