It is the middle sentence:
'I like simple things, such as going out for a meal or going shopping.'
The difference with the first sentence is one of style and of grammar. It is poor style to change the verb type from a gerund to an infinitive in a matched pair of actions such as two things you like doing. Also, because you like 'things' these should be nouns, because things are nouns. If you remove the gerund from the first sentence this error becomes more obvious.
'I like simple things, such as to go shopping.'
The last sentence is correct but odd. Here you are not using the two-part verb 'going shopping',but a 'going to' future. If you like 'going to shop' it means that you like getting ready to shop, but not necessarily the shopping itself.