Every Ukrainian town has a downtown and parks with plenty of room to stroll. As in much of Europe, people tend to walk and use public transportation whenever possible (cities are densely populated). Cycling is becoming increasingly popular as well.
Swimming and sunbathing
Almost every Ukrainian town also has lakes or rivers nearby where you can swim or sunbathe. Kiev, for example, has miles and miles of free public beaches along the central Dnipro River, as well as lakes scattered around outlying residential areas of the city. What a treat!
Watch for polar bear dippers and ice fishers in the winter as well.
Another thing Ukrainians love to do is talk. While strolling, in cafes and restaurants, or at home. Over a cup of tea or coffee (or other drinks). Conversation tends to be light, relaxing, humorous, and sometimes philosophical.
Popular outdoor sports in Ukraine are soccer, volleyball, badminton, table tennis, and hiking (walking in the forest). Fitness clubs have appeared all over the place. Yoga and martial arts are quite popular as well. Mountain climbing and rock climbing clubs can be found. Scuba diving, yachting, and even golf have recently become available for the "elite."
Picnics and shish-kabobs
Many Ukrainians enjoy picnics outside at almost any time of year. Picnics often involve shish-kabobs or barbequed meat, homemade salads, and, of course, alcohol.
Ukrainians love to sit around fires at night and snack, drink, and sing songs to a guitar. It's one of those quintessential Ukrainian things that you see everywhere.
Increasingly popular in Ukraine are all sorts of extreme sports (hangliding, bungee jumping, river rafting, downhill mountain biking, spelunking, etc.), and, more generally, all forms of active recreation (hiking, biking, boating, horseback riding, skiing, etc.). After the fall of the Soviet Union Ukraine has gradually become aware of all the urban fads worldwide and is gradually catching up. Another factor is the increasing (but still inadequate) availability of imported sporting goods.