do 后面有_ing 的形式还很常见呢！

你这里的：do sightseeing = do some sightseeing = go sightseeing

意思是“进行观光或游玩”

跟 do some shopping = go shopping  “买东西”

还有 do some swimming = go swimming  “游泳”  是一样的句式。可以说是固定搭配了。

go doing 经常是表示户外的活动,而则表示室内活动.

如： do some shopping=go shopping可以理解为shopping可在室内也可在室外....

类似的do some -ing短语：

to do some shopping 买东西

do some shopping 买东西

do the shopping 买东西

to do the shopping 买东西

do shopping for the spring festival 买年货

do window shopping 逛商店,看橱窗

do some market research for 为...做市场调查

do (some) cleaning 扫除

do some cleaning 做(些)清洁工作

do some good 有益于,有帮助

do some reading/sewing/climbing/swimming/riding

希望能帮到你！