Although the default word for "at" in Russian is в, there are many nouns that are used instead with на. Some of them group into broad categories, and some of them just have to be memorized one at a time. Among the broad categories are:
Classes and other things you attend
на заня́тии
at class
на ку́рсе
at class
на ле́кции
at a lecture
на пра́ктике
at the practicum
на репети́ции
at rehearsal
на семина́ре
at a seminar
на собра́нии
at a meaning
на экза́мене
in a test
на бале́те
at a ballet
на вы́ставке
at an exhibition
на конце́рте
at a concert
на спекта́кле
at a show
на о́пере
at an opera
на пье́се
at a play
Things that must simply be memorized
на база́ре
at the bazaar
на вокза́ле
at the train station
на да́че
at the summer house
на по́чте
at the post office
на рабо́те
at work
на фи́рме
at the company
на ры́нке
at the market
на дискоте́ке
at the disco
на дне рожде́ния
at a birthday party
на пра́зднике
at the holiday party
на войне́
at war
на би́рже
at the stock exchange
на консульта́ции
at a tutorial
на куро́рте
at the resort
на скла́де
at the warehouse
на заво́де
at the plant
на фа́брике
at the factory
на ста́нции
at the station
на ку́хне¹
in the kitchen
на факульте́те
in the department
на кани́кулах
on vacation
на экску́рсии
on an excursion
на Украи́не
in the Ukraine
на Камча́тке
in Kamchatka
на Аля́ске
in Alaska
¹ This word is undergoing a shift from being a на word to being a в word.
Points of the compass
на ю́ге
in the south
на се́вере
in the north
на за́паде
in the west
на во́стоке
in the east
Bodies of water
на Байка́ле
at/on Lake Baikal
на Во́лге
on the Volga, on the shore of the Volga
на Неве́
on the Neva, on the shore of the Neva
на мо́ре
at the sea, at the seashore
на реке́
at the river
на пруду́
at the pond
на о́зере
at the lake
Mountains and mountain ranges
на Кавка́зе
in the Caucusus
на Ура́ле
in the Urals
Wide, flat places
на о́строве
on the island
на у́лице
on the street
на бульва́ре
on the boulevard
на проспе́кте
on the avenue
на берегу́
on the shore
Problematic words
The usage of в-на may not be stable for the following words: станция, комбинат, опера, балет. At the moment I suspect that when someone means "in the building where the opera/ballet is" they tend to use в, but when speaking of the event itself they use на. If one specifically means "inside" a station, then they tend to use в, but when talking about going "to" a station as the goal of motion, then they tend to use на.