Learn Hardcore Chinese: míngtiān wǒ sòng nǐ dào túshūguǎn.

Chinese usually relies on time words to show tense. Here, 明天 (tomorrow) makes the sentence future. Adding 会 is optional and just adds a “will/likely” feel: 明天我会送你到图书馆.

What does 送 mean in this sentence?

送 has several meanings; here it means “to escort/drop off/see someone to a place.”

Escort/drop off: 我送你到图书馆 (I’ll take you to the library).
Deliver: 我把包裹送到你家 (I delivered the package to your home).
Give as a gift: 我送你一本书 (I’ll give you a book).

Why use 到 and not 去? What’s the difference?

到 + place emphasizes reaching/arriving at the destination.
去 + place emphasizes going toward the destination. With 送, both are fine; 到 slightly assures arrival. Examples:
我送你到图书馆.
我送你去图书馆.

Can I say 送你到图书馆去?

Yes. Adding 去 at the end (…到图书馆去) is common in speech and emphasizes the outward direction. All three are acceptable: 送你到图书馆, 送你去图书馆, 送你到图书馆去.

Can I omit 到/去 and say 送你图书馆?

No. After 送 + person, you need a word marking destination (到/去). 送你图书馆 is ungrammatical. Compare:

送你到图书馆 (correct)
送你一本书 (correct, “give you a book” — different structure)

What’s the word order around the person and the place?

Standard pattern: Subject + 送 + person + 到/去 + place.

明天我送你到图书馆. Don’t say 送到图书馆你. An alternative with 把 is possible (see below).

Where can the time word go? Is 明天我… the only option?

Time can go at the start or after the subject:

明天我送你到图书馆.
我明天送你到图书馆. Both are natural.

Do I need a measure word with 图书馆 here?

No, because it’s a destination, not something you’re counting. If you do count, common measure words are 座/所/个:

一座/一所/一个图书馆.

How do I add the means of transport?

Place the transport phrase before 送:

明天我开车送你到图书馆 (I’ll drive you…)
明天我骑车送你到图书馆 (I’ll bike you…) You can also say: 我们坐地铁去图书馆，我送你到门口.

How can I make this an offer politely?

Add a softener or a question tag:

明天我送你到图书馆吧.
明天我送你到图书馆，好吗？
要不要我明天送你到图书馆？ For more formality, use 您: 明天我送您到图书馆吧.

How do I negate or say I can’t?

我不送你到图书馆 (I won’t; refusal/habitual).
我不能/没法送你到图书馆 (I can’t; lack ability/permission).
我没送你到图书馆 (I didn’t; past negation).
我送不了你到图书馆 (I’m unable to; can’t manage to).

What’s the difference between 送, 带, 陪, and 接?

送: escort/drop off and leave (我送你到图书馆).
带: take/bring someone along (我带你去图书馆 = I’ll take you there with me).
陪: accompany and stay with (我陪你去图书馆 = I’ll go with you and keep you company).
接: pick up (我去图书馆接你 = I’ll pick you up at the library).

Can I use 把: 我把你送到图书馆?

Grammatically yes: 我把你送到图书馆. With people (especially 你), 把 can sound a bit forceful/controlling unless context justifies it. It’s very natural with third persons or things: 我把他送到医院; 我把书送到图书馆.

Any pronunciation or tone tips?

Pinyin and tones: míngtiān(2-1) wǒ(3) sòng(4) nǐ(3) dào(4) tú(2) shū(1) guǎn(3). Third tone before a non–third tone is usually pronounced as a “half-third” (low) in flow, so nǐ before dào sounds low.

Can I add 了?

Use 了 for completed actions, not future. After it’s done, you can say:

我已经把你送到图书馆了.
我送你到图书馆了 (context-dependent). Don’t use 了 with 明天.

Is 到 here a verb (“arrive”) or a preposition?

Functionally it marks the destination after a motion/causative verb like 送. You can think of it as “to/till (a place).” In resultative form, you might hear 送到了图书馆 (emphasizing arrival).

Can I drop the subject 我?

In conversation, if context is clear, yes: 明天送你到图书馆. But including 我 is clearer and more standard.

Can I replace 你 with a thing?

Yes, and the meaning changes accordingly:

明天我送书到图书馆 (I’ll deliver a book to the library).
明天我把书送到图书馆 (with 把).

Is 送你在图书馆 acceptable?

No. 在 marks a static location (“at”), not a destination after motion verbs. Use 到 or 去: 送你到/去图书馆.