I want to go for wine and tapas, it's correct to say this? - I feel like wine and tapas. - I feel like I want wine and tapas. - What about going for wine and tapas?
Yes, you can say
1) I feel like having wine and tapas.
2) I feel like going for wine and tapas.
3) I feel like wine and tapas.
The third sentence uses an understood gerund, whether it's eating or having, etc. after feel like.
explains that using feel like before a food is "perfectly grammatical" and "not at all substandard". That the object of like is the understood (i.e., elided) gerund eating and that the object of eating is the food substance.
feel like something
to have a desire to do or have something:
I feel like Chinese food.
If you feel like something, it can also mean that you want to have it or to do it.
I feel like pizza for dinner.
See also the dialog at ESL Fast:
A: Let's go out to eat.
B: That sounds like fun.
A: Where do you want to go?
B: Let me think a minute.
A: I feel like Chinese.
B: That sounds delicious.
I don't know how wine and tapas feels.
I don't know that I would like to feel wine and tapas.
If I wanted to both eat tapas and drink wine, I would want to have some wine to drink and some tapas to eat.
Therefore; either form, "I feel like I want to have some wine and tapas;" or, "I feel like having some wine and tapas," would work and preserve the "I feel like" construction.