In the manga and anime it is well established that Ami loves swimming as a relaxation. Swimming is apparently one of the few things her father taught her before he left, and she's quite good at it. At one point in the S series of the anime she races with Michiru and would probably have won the first round if she hadn't prevented herself from doing so out of fear of offending Michiru.
She is also shown in the R series to be very good at chess, she's apparently been playing chess with an old man she knows, and competes in a big competition, making it through to the final round and competing against one of the youma controllers, Beruche, and again would have won, except this time Beruche cheated.
It is often believed that Ami is not a well rounded person because she has little to no interests outside of studying. While chess is a very studious subject, and she doesn't have as many extra-curricular activities as the other girls, she does have some, and knows the benefits of relaxing. She's often shown reading, and while the things she reads are often study-related, to her this seems to be a form of relaxing, to study something different, and to stretch her mind
Once the girls are in high school, in Stars, she joins the Computer Club as an after school activity.
In PGSM there are fish in her bedroom, and in the SuperS manga she picks up a fish to have as a pet. In PGSM swimming and chess are not explored as options, she discovers a passion for knitting after having to knit for class, and makes all the senshi gloves, and Luna a scarf. It's also shown that she might not be a very good cook, given in later episodes she makes cookies for Nephrite which apparently taste awful, but he really likes, which makes me wonder if she made them bad deliberately because she knew Dark Kingdom food was awful?