Translation:It's up to you!
I agree. There are any number of possible English translations or conversational equivalents for 随便你 besides 'It's up to you.' The idea conveyed is that you are being given the choice. Some additional equivalents: (do) as you like, (do) as you wish, (do) as you please, it's your choice, the choice is yours, it's your decision, it's your call, whatever you like, whatever you want, suit yourself. I'm not in favor of accepting 'have it your way' or 'please yourself' which though they tell someone to make his or her own choice, seem to express personal displeasure with that choice.
Besides it's use in other polite or friendly expressions, such as 随便吃吧, help yourself (=eat what you like), 随便 can also be used to mean willful, arbitrary, or deciding one sidedly, without properly considering others: 说话随便, not be careful about the way one talks. The Chinese examples are from the top notch Pleco dictionary app.
"As you wish" is not an exact synonym for "it's up to you". Tarkin: "Lord Vader, how should we torture the prisoners?". Vader: "It's up to you." Tarkin: "Let's water board them then!" Vader: "As you wish."
Whether it's also a valid translation is a different question, about which I have no idea :-)
Hey guys, advanced-level speaker here. Be careful when using this phrase! If used with an impatient tone, it means more like "Whatever! I don't care!", like when you're fed up with someone and want the conversation to be over. Really a better, less dubious phrase would be “看你啊” (kan4 ni3 a5), meaning "It depends on you" or "It's up to you", like when you're kindly offering to let someone else make a decision.
It's a hard one to translate (I prefer a straight "whatever" in the teenage style or how/which/where/ever" depending on the context). It's really an umbrella term of ambivalence - a desire to minimize the importance of an option or situation. However, as broad a term as it is in Chinese, it is extremely important phrase, used a lot, and surprisingly useful. Even after I left China I continued using it even when speaking English to Chinese students as a convenient way too summarize my ambivalence