This weapon is inferior compared to the starting MP5 H&K or the Scorpio (which is still worse than the MP5) both in range as well as damage. If you happen to collect a number of these guns during your travels, be sure to turn them into the quartermaster in exchange for better supplies.
An UZI can be found on a raider inside the gate house, in front of the Brahmin Wood compound. Another UZI-toting raider is inside the road block, another in the ruins. Two more are inside the raider base.
A single UZI can be found in Rock Falls, on a raider near the mined field on the east side of the complex. Watch out, his UZI is loaded with JHP rounds.