For dinosorus footprints I don't advice to go there (we couldn't be sure!) but I liked to see Sataplia cave. Cave is nice , also it is nice walking tour. But for open to the cave you must call some people before you go... It is not open always.
Walk uphill through the Jewish district on the Gapovonis kucha and you’ll reach a church & cemetery built on a promontory above the city. This is “The Pantheon”, where famous Kutaisi people are buried. The graves themselves are quite interesting, even the modern ones, and the sunset views over the town are beautiful.
The former Jewish district of Mtsvane Qvavila north-east of the main town square can be a quite nice strolling area in late afternoons - once imposing, now depressing & dusted houses margin the narrow bumpy streets which lead uphill. The first synagogue seemed like a fortress because of its high fences, while the second looked like as if closed for an eternity.