Translation:I go to the movie theater often.
良い (いい) is the い-adjective meaning "good". The thing is that you can modify adjective to become adverbs. い-adjective lose their final い and is replaced with く... The tricky part here is that 良い is irregular, and can change to いい to よい! This is one of these cases.
To recap, adverbial form of 良い is 良く (よく)
It may have to do with the difference between "often" and "alot". Saw this come up elsewhere in Duo when たくさん was used to mean "alot" in the sentence "I swim alot in summer". I think that Duo (and maybe real Japanese? I'm doubting myself now too...) likes to strictly use たくさん for "a lot" and よく for "often"?
You can put it before the verb, as well. It doesn't really have to do with being near the word its modifying. If you say "yoku" first, it feels to me like you're emphasizing the fact that you go often, whereas if you put it before the verb, it feels to me like you're just making a statement about something you do often.
Because "a lot" isn't a true synonym of "often" in the sense being used here. According to wordweb, "a lot" means "to a very great degree or extent" or "lot" by itself "a large number, amount, or extent" whereas "often" means "many times at short intervals, or frequently". It is a bit nitpicky, but it seems to me that "a lot" basically means that there are many instances in general, but "often" means that those instances are close together within a short time as compared to over time.
"a lot" also has other meanings too. Consider "I drink a lot of coffee (volume)" and "I often drink coffee (frequency)"
With that point considered, the Japanese words たくさん and よく seem to line up with the difference between "a lot" and "often" respectively as far as I see.
へ indicates direction, and means something like "toward" or "to" when describing motion.
に has a bunch of uses. Any time you can use へ, you could use に (the reverse is not true) where it means "to." It can also mean "at" or "in" to specify location (of a person or thing) with a stative verb, and can mark indirect objects.
で specifies locations of action verbs, and means "at" or "in" but answers the question "where is the action taking place?" Compare いえにいます "I am at home" and いえで食べます "I eat at home"
If you want "good" (the adjective) to describe the cinema, you'd want to use いい to modify the noun; i.e. you'd have いいえいがかんに行きます。The adverb form of いい is よく which would mean "well" and describe the action; i.e., えいがかんによく行きます。(I'm not sure how one goes to the cinema poorly, but that's a topic for another thread).
From what I've read, adverbs of time/frequency (such as "often") come at the beginning of the sentence, while adverbs modifying verbs (like "well") come immediately before the verb, so there's some word-order clues to what's happening here. Note that these two words are homophones -- like here and hear, you'd know what a speaker means by how it is used.