Everything that a tourist would want to see within Gori is easily accessible on foot; the city center is compact.
To get to nearby Uplistsikhe, however, it is best to hire a taxi. Taxis are easy to find around the main square and drivers will be willing to wait for you while you explore Uplistsikhe so that they can drive you back to Gori once you have finished. The whole taxi ride, including waiting, should not cost more than 25 lari and drivers will go as low as 15 lari if you are a hard bargainer.
Public transport to Uplistsikhe is much cheaper at 1 lari each way. Buses go from Stalin Avenue to the village on the opposite side of river. A train departs to Uplistsikhe from Gori at around 10AM and returns around 5PM. A bus also makes the trip, departing Gori's bus station once around 9AM and again at noon, returning around 3PM.
If you are driving, head south in Gori on Stalin Ave across the Mtkvari River and turn left on the second main cross-street not the one running right along the river. This road will take you through the village of Khidistori, where you should try to maintain a straight course, bearing to the left if at a fork, and past the village you should approach Uplistsikhe. If you are feeling lost, ask anyone for directions try "sahd-ah-rees oo-plee-see-khay?" and they will point you right.
