Ukraine is a very beautiful country, but my favorite city is Lviv with it's old architecture, narrow srteets and coffee aroma. Also you may spend few days in Kyiv, Odessa, Yalta, Kharkiv..
Crimea is all the time a good idea. Try to avoid travelling in peak season i mean to say particularly in the month of July and August. It will more expensive and over crowded. Winter is a low season. So the Peninsula becomes really wonderful to get around, however less exciting perhaps. If you like nature, you might also want to see Carpathian Mountains. Even if you don’t skate the area itself is truly superb in winter. And avoid high season around the NYE.
If you are travelling in winter get well prepared. Don’t forget to carry warm cloths and shoes. Be ready that if we face heavy snowfalls, the roads can be blocked and the airports can be temporarily closed. So stay stretchy. Some scenery spots may become less picturesque if the winter is grey and snowless, so don't be disappointed