Japanese is such a cool language to be able to speak! The closest translation in Japanese to the English I could find to "I hope you feel better" is as follows:
"Watashi wa anata ga yoi kanji okitai"
It is written in Japanese as follows:
Alternative ways to wish someone well
If you do not speak Japanese fluently, or are unsure of how to pronounce the more complex sentence above. It may be easier to say the phrase "Get well soon" which is pronounced:
"Hayaku yokunatte ne"
It's good to bear in mind that there aren't always direct translations for words in other languages so it's sometimes better to find the phrase which is most commonly used in another language to get across the same message.
In Japanese the most common way to wish someone well/hope they get better soon translates into English as "take care (of yourself") and the below video shows you how to pronounce this correctly: