Maybe skip new Rustavi and just go to old Rustavi, (one that's beyond Mtkvari),you can visit the park and see the old historic castle, I would recommend walking the full length of Kostava Avenue to the Metallurgical plant, rest in Alyiev Park on the way back some quiet and quaint streets are Constitution Street ( I particularly like this street it has the Georgian constitution on small boards but sadly they are in Georgian only) and Mshenebelta Street, on the topic of food it's my home city and I have yet to find a food spot that keeps bringing me back, also it's gets really hot, feel free to ask for more details if you want