"Going to Beijing for a visit" or "taking a trip to Beijing" are both common ways to say "去北京游玩" in Engpsh.

The source of these phrases is the Engpsh language and they are commonly used to describe the act of travepng to Beijing for the purpose of sightseeing or vacationing.

Here are some example sentences using these phrases:

"I'm planning on going to Beijing for a visit next month." (我下个月打算去北京游玩。)
"We're thinking about taking a trip to Beijing over the summer." (我们在考虑夏天去北京游玩。)
"Have you ever been to Beijing? I'm thinking about going for a visit next year." (你去过北京吗?我在考虑明年去北京游玩。)
"We're going to Beijing for a visit next week. We can't wait to see all the sights and try the local food." (我们下周去北京游玩。我们迫不及待想要看看各种景点,还有尝尝当地的食物。)