Learn Hardcore Chinese: Yínháng zài wǒ gōngsī fùjìn.

银行 (the subject) + 在 (locative verb/preposition “at/in”) + 我公司附近 (the location, with 附近 “vicinity” as a location noun).
This pattern states where a known subject is.

Do I need 的 between 我 and 公司? Are 我公司, 我的公司, and 我们公司 all okay?

我公司: grammatical but formal/business style (“our company” in corporate writing). Common in formal Mainland/Taiwan contexts; a bit stiff in casual speech.
我的公司: literally “my company,” often implying ownership. It can mean “the company associated with me,” but many speakers avoid it for “my employer” to prevent the ownership implication.
我们公司: the most natural everyday way to say “my company (where I work).” So in conversation, 银行在我们公司附近 is most idiomatic. If you truly own the company, 银行在我的公司附近 is perfect.

Can I say 公司的附近?

Normally no. Use 公司附近 (no 的) because 附近 functions as a location word after a noun. Add 的 only when the phrase modifies a following noun:

公司附近的银行 = “the bank(s) near the company.”

What’s the difference between 附近 and 旁边? Which one should I use?

附近 (fùjìn) = “nearby; in the vicinity” (same general area; not necessarily adjacent).
旁边 (pángbiān) = “right next to; beside” (immediate adjacency). Use 附近 for general nearness: 银行在我公司附近. Use 旁边 if it’s truly next door: 银行在我公司旁边 (also 旁边儿/边上 in northern speech).

Could I rephrase it with 离 to express distance?

Yes. Use A 离 B 很近/不远:

银行离我公司很近 (“The bank is very close to my company.”)
银行离我公司不远 (“The bank isn’t far from my company.”) This emphasizes distance, while 在…附近 emphasizes location.

How do I say “There is a bank near my company” (introducing existence), not locating a specific bank?

Use the existential pattern 在 + Location + 有 + N:

在我公司附近有一家银行。 Or without 在:
我公司附近有银行。 Include a classifier to be specific: 一家银行 (“a bank”).

Is 在 a verb or a preposition here? Why not use 是?

在 functions as a locative verb/preposition meaning “to be at/in.” Chinese doesn’t use 是 to link a noun to a location, so you say 银行在…, not 银行是…. You can use 是在… only for contrast/emphasis:

银行是在我公司附近，不是在学校附近。

Should I add 里 or 边 after 附近 (e.g., 附近里, 附近边)?

No. 附近 already means “the vicinity” and stands alone: 公司附近. Don’t attach 里/边 to 附近. (With other location words you might add parts like 旁边/里面/外面, but not with 附近.)

How do I pronounce 行 in 银行? Is it xíng or háng?

In 银行, 行 is háng (second tone). Use xíng when it means “to be OK; to do” (e.g., 行吗？) or in verbs like 进行 (jìnxíng).

What measure words should I use with 银行 and 公司?

一家银行 / 一家公司 are the most natural.
个 (一个公司) appears in casual speech but is less precise.
一间公司 is also heard regionally; for banks, 家 is standard.

Any tone-sandhi or pronunciation gotchas in this sentence?

Third-tone sandhi: a third tone becomes second only before another third. That doesn’t occur here, so 我 (wǒ) stays third.
附近 is two fourth tones (fùjìn), and 在 is fourth tone (zài).

How can I emphasize that it’s right nearby?

Add 就 before the location:

银行就在我公司附近。 (“The bank is right near my company.”) You can also use the distance pattern: 银行离我公司很近.

Is 银行在我公司附近 natural in everyday speech?

Yes, but it sounds formal because of 我公司. In casual speech, 银行在我们公司附近 is more natural.

Can I front the location for emphasis or as a topic?

Yes. Topic-fronting is common:

在我公司附近，银行很方便。
Or the existential form: 在我公司附近有银行。 Avoid ungrammatical orders like 我公司附近在银行. The core patterns are N 在 Location and 在 Location 有 N.