Hi, I'm getting a little confused about the many ways to say "to".
Can you pretty much say:
Nach: to cities or countries not always. If the country is not neuter, you use "in": in den Irak in die Schweiz in die Niederlande
zu: to people yes, but you can also go "zu" things that are not people.
an: to somewhere close Example? I don't think it has to do with how close the place is: Ich gehe in das Zimmer. You can say the above even if the room is very close. Furthermore, "an" can be used figuratively: Der Preis geht an Klaus. It can also be used for long distances. Ich schicke eine Karte an meinen Freund aus Deutschland nach Kanada.
in: to a large place, "in die Stadt" It need not be large. "In" is used when you are literally going into a place: Ich gehe ins Kino. Ich gehe in die Küche.
auf: to an open-air place, "auf den Markt" It need not be open-air. You use "auf" here because you are not going "into" the market. Similarly, you can say Ich gehe auf eine Party.
"an: to somewhere close" Although I've seen this description elsewhere, I find this wording unhelpful. "An" refers to either position (being at, beside, or on) or motion (moving to a position at, beside, or on). (You can see it's cognate to 'on'.) 'An' means beside something without regard to relative spatial position, which differentiates it from 'in' and 'auf' (cognate to 'up'). 'Auf' means simultaneously beside and on top, and 'in' denotes going inside the object. The English word 'on' itself sometimes implies 'auf', sometimes' 'an'.
Hence 'an' bodies of water, 'an' a beach, 'an' a windows and walls; but 'auf' pieces of ground (streets, islands, "the countryside". German thinking is "to beside" a beach, not "onto" a beach; and "onto a street", not "into" a street.