The way I use is that I don't run and I plant many flowers and trees and clear up my ground from items and patterns.It works really well and fast in the Spring and Summer,but do not time travel and it won't work.Be patient.
Your grass will gradually re grow for every day you go online. For easy results. Get someone to dupe you lots of Gold Roses, plant them on the run down areas of your town.. Then save, talk to Rover, Time Travel to the next day, then go on, save. Talk to rover, time travel to the next day... Etc.... Once you have gone through about 4-6 months in this method (will take about 2-3 hours) then your grass will basically be restored.