This morning, I received the above question. In the sentences, "I like traveling in this city" and "I like to travel in this city," "like" is the conjugated verb. In the first sentence, "traveling" is a gerund. In the second, "to travel" is an infinitive. The verb "like" takes both gerunds and infinitives, which means you can say "I like traveling in this city" or "I like to travel in this city." The sentences are almost identical in meaning.
Similarly, there is almost no difference between I like to cook Chinese food and I like cooking Chinese food. You can use the infinitive to cook or the gerund cooking. Not all verbs allow both the gerund and the infinitive. For example, you can say I enjoy preparing, but you cannot say "I enjoy to prepare." You can say "I want to prepare" but not, "I want preparing...." I don't know that there is an easy rule to follow here, but here is a list of verbs followed by a gerund and verbs followed by the infinitive: https://www.engvid.com/english-resource/verbs-followed-by-gerunds-and-infinitives/ The article also contains a list of verbs whose meanings change depending on whether they are followed by the gerund or infinitive. Thanks for an excellent question! Also, check here: https://www.thoughtco.com/list-of-verbs-followed-by-gerund-or-infinitives-1211246 Have a great afternoon!