The city is relatively small, you can walk around on your own, but it is advisable to have a map of Borjomi. If you need a map of Borjomi in Russian, you can go to the local tourist office, where at the same time find a suitable place to stay and have lunch.
It will also help you with the question of which Borjomi area to stay in. The fact is that Borjomi's districts are not officially delineated. Unofficially the area in the center of Borjomi is its main square, as well as a peculiar boulevard along the river, dotted with exchange offices, banks, and catering establishments.