I found myself wondering about this the other day. Beijing isn't a central location. There are other more populous regions.
And my understanding is that the CCP has a complicated relationship with Imperial history and often tries to distinguish itself from the old imperial system. So why did they not pick a 'new' capital? What was the decision process that made Beijing the choice, and were any other cities considered?
Beijing was indeed a new capital in 1949, because for the previous 22 years, China had been governed from either Nanjing or Chongqing.
There were two reasons the capital was returned to Beijing: one practical, one symbolic.
The practical reason is that the Chinese Communist Party's power base in the Chinese Civil War (1946-49) was in northern China. From 1936 to 1947, Mao's Communist government was based in the Shaanxi town of Yan'an. From here, the CCP recruited 1.2 million party members and an army of over 1 million. In 1947, Yan'an was evacuated during a Kuomintang offensive targeting it, and most of the government moved into Manchuria, which is where the first big cities were captured. The CCP and People's Liberation Army both grew to over 2 million during the Manchuria campaign, with most members and soldiers being northerners. After the Communists' staggering success in the Manchuria campaign (over 1 million Kuomintang soldiers killed or captured at a cost of just 100,000 Communist casualties), the war basically turned into an unstoppable communist advance from the Communist power base in the north to the south of China. In Jan 1949, Beijing became the first city south of the Great Wall to fall to the Communists, and Mao, impatient to begin the work of establishing a real national government, instantly began plans for a pre-parliament (the Chinese People's Political Consultative Conference) that would draft a constitution, pick a flag, a national anthem (they chose 'March of the volunteers' which has the distinction of being the only national anthem originally written for a made-for-cinema patriotic musical) and so on. All of this unfolded even as millions of KMT and Communist soldiers fought across the North China Plain and into central and southern China. Much of this happened before the seat of the KMT government, Nanjing, had been captured. So from a practical perspective, Beijing was just the first real city available.
The symbolic reason is that Mao very deliberately sought to distinguish himself from the Kuomintang regime of Chiang Kai-shek. Chiang had already played the nationalist card of 'Beijing is really a foreign city and not fit to be China's capital' back in 1927 when he seized power in the Northern Expedition and established his new government in Nanjing. By 1949, 'Nanjing' was synonymous with corruption, warlordism, and ineffectual administration. Thus, Mao needed to reject the symbolism of Nanjing, and since Beijing had been a symbol of peace and strength in past eras, there was no reason why it couldn't be again. While there was a danger of being compared to the Qing, Mao liked to symbolism of the imperial capital for its strength. For example, when he held a ceremony formally inaugurating the new People's Republic of China in Oct 1949 (which, incidentally was before the CCP had actually won the war!) he gave his speech from atop the Gate of Heavenly Peace at the Forbidden City - a symbol of imperial power. You can see elements of Mao's skill as a marketing genius elsewhere - he rebranded the Red Army as 'the People's Liberation Army's in 1946, he renamed 'the Republic of China' to 'the People's Republic of China' etc. (These terms link to how Mao rebranded the CCP as a nationalist, rather than Marxist, organisation, promising to fulfil Sun Yat-sen's principles of nationalism and people's livelihood - values that the KMT ostensibly stood for but had failed to realise.)