How do I say "Why not both" in Mandarin?
为什么不两者兼得? - this is more likely to appear in books or writing.

为什么不两样都做? - this sounds more natual. 

If you choose to say the second one, you may want to change it a little bit by saying 为什么不两个地方都去？

But I would say 不如两个地方都去！as this sounds more energetic, simpler and positive.

Reference: Native speaker