Only the prepositions in and at work in this sentence. On does not work in combination with the noun restaurant.
The indefinite article a is indeed used if the restaurant has not yet been mentioned by the speaker before. It is also used when speaking about a restaurant in general:
I like eating at a restaurant.
In this case the plural of the noun can also be used (with a zero article):
I like eating at restaurants.
You use the definite article the if the restaurant is known in the context or if it has been mentioned before.
I like eating at the restaurant on the corner.
In that sentence it is clearly known which restaurant is being spoken about because it is specified by on the corner.
Or known via context: Suppose the speaker works at a restaurant. If that person then talks about the restaurant, the hearer will know which restaurant is being talked about because the speaker works there and the hearer knows this.
You cannot leave out the article in your sentence.