He wasn't at peace at the end of TDK. His loved one was killed, Gotham was in chaos, Harvey Dent was a murderer and was killed, and Batman itself had to take the blame. He was forced to retirement, but he wasn't ready for it, which is why he couldn't be at peace. In TDKR, Gotham knows the truth and understand his sacrifice. People can now build the city again. A war is over, hope is back, his mission is over. He inspired not only Blake, but also Selina, Foley, and it's likely he inspired a lot of other people. His legend is strong enough to ensure that someone will take over after him, and the citizen themselves will be ready to fight for their city, because he gave them hope, he show them what heroism and altruism is about.