"Patronise" is formal and the sentence does not use it correctly. Informal options: "He often goes to this restaurant and has tea and cake." "He's a regular customer at this restaurant. He has tea and cake there." Of the options that Mohammed gave, "frequent" is correct but is also formal. The others are not correct.

Hello there, hope you are doing well. I just did a quick research about the first part of your question and then I found out that this word is considered as formal. Here it is the definition of that word in Oxford Learners' Dictionary: patronize something (formal): to be a regular customer of a shop/store, restaurant, etc. The club is patronized by students and locals alike. As you saw, this word is "formal". *Some of the options which can be used instead of that formal verb are: *frequent, haunt, attend, visit; subscribe to, join, hang out at (informal)*