Right answer: a las
This is a good example of the usage of prepositions and articles in a sentence.
Firstly, let’s begin with the prepositions:
The preposition is a word that relates the elements of a sentence. Prepositions may indicate origin, destination, address, place, medium, point of departure, reason, etc.
In the Spanish grammar is defined as the invariable part of the sentence that joints words denoting the relationship they have with each other and introduce complements.
The prepositions in Spanish are: a (to), ante (in the face of), bajo (under), cabe (fit), con (with), contra (against), de (of), desde (since), durante (during), en (in), entre (between), hacia (towards/to), hasta (until/to), mediante (through), para (for), por (by), según (according to), sin (without), so, sobre (over), tras (after/behind), versus and vía (via).
On the other hand we have the articles:
The article is just a word that clearly indicates the gender and the number of the noun. Its function is to modify the noun it introduces.
The articles may be:
Variable Articles:
Defined Articles:
Singular Masculine: el
Singular Femenine: la
Plural Masculine: los
Plural Femenine: las
Indefinite Articles:
Singular Masculine: un/uno
Singular Femenine: una
Plural Masculine: unos
Plural Femenine: unas
Invariable Articles:
Neutral: Lo
Contractions: al (a+el) and del (de+el)
Now, in this case of the sentence, we are talking about going to a place (a destination), therefore we should use the preposition a.
In addition, the destination is fiestas de Martín (Martín’s parties), this means it is defined.
Fiestas is a plural feminine noun, therefore (according to the list above) we must use the defined article las
Hence, the correct way to write this sentence is:
Nadie va a las fiestas de Martín porque son aburridas.
Nobody goes to Martin's parties because they are boring.
