"Today is a good day to go shopping."
Translation:Hoy es un buen día para ir de compras.
"ir" is typically followed by "de" when the following phrase is a noun-activity, such as shopping, vacationing, etc. Ir is followed by "a" when the following is a noun-place, such as "cine" or "escuela". Ir is also followed by "a" when the next phrase is an infinitive verb.
ir de compras = to go shopping (noun activity) ir al cine = to go to the movies (noun place) ir a comprar= to go buy (infinitive verb)