The COVID-19 had a huge impact on the transportation industry. In the post-epidemic stage, intercity transportation will face great challenges as places are unsealed, tourism and other service industries begin to recover, and residents’ travel demand gradually increases. An in-depth study of residents’ intercity travel behavior during holidays in the post-epidemic era will help restore public trust in public transportation and improve the quality of public transportation services. Based on traditional research on ways of travelling, the study adopted the Complex Network Analysis Theory. The city clusters of Shandong Peninsula were taken as the research region. The research studied the impact of the differences in regional attributes of the cities in Shandong Peninsula on residents’ intercity travel in the post-epidemic times. A dynamic evolution model of how residents choose to travel was built to simulate the changes to their ways of traveling in the post-epidemic era under two conditions, which are: traveling under the government’s supervision of intercity travel and traveling under the government’s optimization of intercity travel conditions. The conclusions drawn from the analyses of Complex Network Theory and Evolutionary Game Theory are as follows. First, in the holiday intercity travel in the post-epidemic times, the neighboring cities of Shandong Peninsula are closely connected, thus traveling between neighboring cities dominates intercity travel. Second, the travel network concentration of residents on long-term holidays is lower than that on short-term holidays, and the migration intensity of residents is higher than that on short-term holidays, while the willingness of residents’ migration on short-term holidays is higher than that on long-term holidays. The willingness to migrate on holidays is generally lower than that before the epidemic. Third, in a normal intercity travel network, the travel between two cities with medium and long distances is mainly by public transport. However, the dominance of public transport will be affected under the impact of the epidemic. In short-distance travel between two cities, private transport is in an advantageous position, and under the impact of the epidemic, this advantage will become more significant. The government can improve the position of public transport in short-distance travel by making optimizations.