Located about 30 minutes from Pyeongtaek is a gorgeous forest and mountain hiking area that isn't overrun by people every moment of the year (but I'm sure it happens). The name is Yeonginsan Natural Forest and it's one of the best places South of Seoul to go and get away from it all because it's NOT on a subway stop.
This gorgeous park can be a hard day of hiking (if you park at the lower free parking lot) or an easy day out with the kids on smooth paths perfect for strollers (if you park at the top in the paid parking area & entrance fee. Worth it. Maybe 3,000 per person). If you are a family with mixed levels of activity, it's the answer you have been looking for. You can drop your avid hikers off at the bottom of the mountain, then drive to the top to lounge about in the forest parks and rec areas while they huff it up to meet you.
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