Here’s a useful map of the locations of Ukrainian military bases (as of 2008) and Russian forces located near Ukraine’s borders. It’s drawn from a new Russian language blog, and due to limited time I haven’t checked the accuracy of the map, I’m afraid. Feel free to note any inaccuracies in the comments.
Note that the majority of Ukraine’s forces are located in Western Ukraine, as the positioning of the forces is left over from the Soviet period, when they were placed so as to maximize Soviet defensive potential against NATO forces. There are two mechanized infantry brigades, a tank brigade, and an artillery brigade in the east, though, as well as airborne brigade and a tactical aviation brigade. Compare this to western Ukraine, where there are five mechanized infantry brigades, two artillery brigades, a tank brigade, a rocket brigade, four tactical aviation brigades, two army aviation regiments, and an air mobile brigade. Also worth highlighting the forces located in the south, near the Crimea: one mechanized infantry brigade, a tactical aviation brigade, an air mobile brigade and an army aviation regiment.
Here’s another map from the same source, with just the Ukrainian forces shown.
The accompanying text notes that the total personnel of Ukraine’s armed forces consists of 184,000 people, including 93,000 in ground forces. These are comprised of four tank brigades, 15 mechanized infantry brigades, 15 artillery brigades, two rocket brigades, 3 air mobile brigades, one airborne brigade, and one air mobile regiment. (Obviously this doesn’t match the numbers on the map) The air force has 160 combat and 25 transport aircraft. Of course, it’s likely that only a relatively small percentage of these units are combat-ready, especially in the air force.