There is always somewhere to go and very inexpensive. Transport in Ukraine is one of the cheapest in the world, and at the same time, the communication network is very wide. For a day without an overnight stay, you can go anywhere, but finding an inexpensive recreation center is not a problem.
Now the tourist component of the Ukrainian business is developing more and more. The competition is growing and the service is improving. Of course, you should not expect that at the recreation center for 100 UAH. per day for a house you will be served five towels and morning fresh juice from passion fruit, but there are also expensive and high-quality hotels and apartments with exceptional service in Ukraine.
Ideas for traveling around Ukraine:

Summer is ahead, so Odessa (and its environs) comes first. Last year I discovered Odessa: beautiful, colorful, and even on the seashore!
We can safely say that one day is not enough for Odessa! Just wandering around the city is interesting, and also the catacombs, the Belgorod-Dniester fortress. But what is there! Even the Privoz market is worth spending the whole day (or night) there, because during my visit one person was closed for the night in a cafe. They just forgot). Those who tolerate off-road well can go to Vilkovo - "Ukrainian Venice". Be sure to try the frog legs! Around Odessa there are many settlements that are considered resorts.One of the most popular is Zatoka, here you can find both a comfortable hotel with its own beach, and rent a room in a wooden house. Many festivals are held in Odessa and its surroundings, so a trip to Odessa can be combined with a visit to one of them. I was there as part of the esoteric festival "Fairytale City", and lived for 10 days in a tent "by the very blue sea", and then I also looked at the city. Also, all kinds of musical events are held here, so there is something to choose according to your interests. The Kyiv-Odessa bus saves you if you need to get to Odessa, but there are no tickets.By the way, this is one of the cases when the bus is faster than the train. In addition, there are many interesting establishments in Odessa, so you won’t be bored!